RANDOM Statement
math.random()方法是用来表示
math.random()方法是用来表示一、概述Math.random()是JavaScript中的一个方法，它被用于生成一个伪随机数。
这个方法可以返回一个介于0（包含）至指定精度的最大整数（不包含）之间的随机数。
精度的默认值是1/2^32，这意味着它可以产生大约1亿个唯一的数字。
这个方法对于生成随机的数值或决定游戏中的事件非常有用。
二、用法Math.random()方法返回一个介于0（包括）和1（不包括）之间的伪随机数。
如果需要更大的范围，可以调用Math.random()两次，例如Math.random()*100。
这将返回一个介于0至99之间的随机整数。
三、特点Math.random()方法的特点在于它的随机性。
生成的数字是基于一个复杂的算法产生的，该算法使用熵源（通常包括当前的时间、系统负载和处理器时钟速度）来产生随机数。
这种随机性使得Math.random()生成的数字在很多情况下具有实际的应用价值。
四、应用场景Math.random()方法在许多场景中都有应用，以下是几个常见的应用：1. 游戏随机事件：在游戏中，常常需要随机事件来增加游戏的趣味性和挑战性。
例如，一个角色可能会遇到一个随机的敌人，或者一个宝箱可能会被打开并获得一个随机的奖励。
使用Math.random()方法可以很容易地实现这些效果。
2. 数值生成：在需要随机数值的场景中，Math.random()方法也很有用。
例如，在模拟系统中，需要生成一系列随机的数据来代表各种情况。
使用Math.random()方法可以方便地生成这些数据。
3. 密码生成：在一些需要生成密码的场景中，Math.random()方法也可以派上用场。
通过将随机数与用户名或其他信息结合，可以生成一个独特的密码，增加了密码的安全性。
五、注意事项虽然Math.random()方法生成的数字看起来是随机的，但实际上它们是有规律的。
这是因为它们是基于算法生成的，而不是真正的随机数。
random函数
一直到"bob5"，我们可以这样写。
i = Math.ceil(Math.random()*5);
attachMovie("bob"+i, "fred"+i, 1);
运行这个代码以后。就会随机的载入一个movieclip，例如"bob3"，放在level 1
random用法：random(x); //注释：x是个正整数
即可随机产生0~x之间的一切整数。而且它是一个函数，不能单独使用。
如a:=random(100)；就是随机产生1个0~100之间的数赋给变量a;
但是如果只用random的话不太好。
因为random函数是随机一个数，然后你再次random的时候还是产生那个数。
end;
writeln;
end;
end.
这两组数据输出的是一样的结果,如果在程序前加上RANDOMIZE(即把大括号去掉)再运行程序,输出数据就不一样了.
RANDOM产生的是伪随机数或者说是用一种复杂的方法计算得到的序列值，因此每次运算时需要一个不同的种子值。种子值不同，得到的序列值也不同。因此也就是真正的随机数了。这也正是RANDOMIZE随机初始化的作用。VB里用NEW RANDOM()来表示初始化。
begin
a:=random(100);(random照常使用)
write(a,' ');
end;
end.
这个程序运行之后打出来的数就是10个不同的0~100之间的数了！所以一般在随机产生数的时候，都要加上randomize不然都是一样的数就不好了。
SAS proc mixed 过程步介绍
Introduction to PROC MIXEDTable of Contents1.Short description of methods of estimation used in PROC MIXED2.Description of the syntax of PROC MIXED3.References4. Examples and comparisons of results from MIXED and GLM- balanced data: fixed effect model and mixed effect model,- unbalanced data, mixed effect model1. Short description of methods of estimation used in PROC MIXED.The SAS procedures GLM and MIXED can be used to fit linear models. Proc GLM was designed to fit fixed effect models and later amended to fit some random effect models by including RANDOM statement with TEST option. The REPEATED statement in PROC GLM allows to estimate and test repeated measures models with an arbitrary correlation structure for repeated observations. The PROC MIXED was specifically designed to fit mixed effect models. It can model random and mixed effect data, repeated measures, spacial data, data with heterogeneous variances and autocorrelated observations.The MIXED procedure is more general than GLM in the sense that it gives a user more flexibility in specifying the correlation structures, particularly useful in repeated measures and random effect models. It has to be emphasized, however, that the PROC MIXED is not an extended, more general version of GLM. They are based on different statistical principles; GLM and MIXED use different estimation methods. GLM uses the ordinary least squares (OLS) estimation, that is, parameter estimates are such values of the parameters of the model that minimize the squared difference between observed and predicted values of the dependent variable. That approach leads to the familiar analysis of variance table in which the variability in the dependent variable (the total sum of squares) is divided into variabilities due to different sources (sum of squares for effects in the model). PROC MIXED does not produce an analysis of variance table, because it uses estimation methods based on different principles. PROC MIXED has three options for the method of estimation. They are: ML (Maximum Likelihood), REML (Restricted or Residual maximum likelihood, which is the default method) and MIVQUE0 (Minimum Variance Quadratic Unbiased Estimation). ML and REML are based on a maximum likelihood estimation approach. They require the assumption that the distribution of the dependent variable (error term and the random effects) is normal. ML is just the regular maximum likelihood method,that is, the parameter estimates that it produces are such values of the model parameters that maximize the likelihood function. REML method is a variant of maximum likelihood estimation; REML estimators are obtained not from maximizing the whole likelihood function, but only that part that is invariant to the fixed effects part of the linear model. In other words, if y = X b + Zu + e, where X b is thefixed effects part, Zu is the random effects part and e is the error term, then the REML estimates are obtained by maximizing the likelihood function of K'y, where K is a full rank matrix with columns orthogonal to the columns of the X matrix, that is, K'X= 0. It leads to REML estimator of the variance-covariance matrix of y, say V. It does not depend on the choice of matrix K. Then the generalized least squares equations, known also from the weighted least squares approach and the GLM procedure,X'(inverse of V)X b=X'(inverse of V)y,where V is replaced with its estimator, are solved to obtain the estimates of fixed effects parameters b.It is assumed that the random effects u and the error vector e are normally distributed, uncorrelated and have expectations 0. Under the assumption that u and e are not correlated, V, the variance-covariance matrix of y, is equal to ZGZ’ + R, where G and R are the variance matrices of u and e, respectively.Estimators of V, the variance-covariance matrix of y, can also be obtained in PROC MIXED by the MIVQUE0 method. For a short description of the method see reference (3), p.506. This method has two advantages over ML and REML; it does not require normality assumption (for computing the estimators) as do ML and REML and does not involve iterations. However simulation studies by Swallow and Monahan (1984) present evidence favoring ML and REML over MIVQUE0. PROC MIXED uses MIVQUE0 as starting values for the ML and RELM procedures.For balanced data the REML method of PROC MIXED provides estimators and hypotheses test results that are identical to ANOVA (OLS method of GLM), provided that the ANOVA estimators of variance components are not negative. The estimators, as in GLM, are unbiased and have minimum variance properties. The ML estimators are biased in that case. In general case of unbalanced data neither the ML nor the REML estimators are unbiased and they do not have to be equal to those obtained from PROC GLM. There are many models involving forms of variance-covariance structure of observations that can not be analyzed using PROC GLM with TEST or PROC GLM with the REPEATED options. PROC MIXED can handle such cases. It also has to be mentioned that PROC GLM was design for analysis of fixed effects models and all computations are done under the assumption that there is only one variance component in the model, the error term. The RANDOM statement with the TEST option can be used to get the right tests in the case random effects are present in the model, but still some printed results, variances and standard errors, will be incorrect.2. Description of the syntax of PROC MIXEDThe PROC MIXED syntax is similar to the syntax of PROC GLM. There are, however, a few important differences. The random effects and repeated statements are used differently, random effects are not listed in the model statement, GLM has MEANS and LSMEANS statements, whereas MIXED has only the LSMEANS statement, GLM offers Type I, II, III and IV tests for fixed effects, while MIXED offers TYPE I and TYPE III. The following is a general form of PROC MIXED statement: PROC MIXED options;CLASS variable-list;MODEL dependent=fixed effects/ options;RANDOM random effects / options;REPEATED repeated effects / options;CONTRAST 'label' fixed-effect values | random-effect values/ options;ESTIMATE 'label' fixed-effect values | random-effect values/ options;LSMEANS fixed-effects / options;MAKE 'table' OUT= SAS-data-set < options >;RUN;The CONTRAST, ESTIMATE, LSMEANS, MAKE and RANDOM statements can appear multiple times, all other statements can appear only once.The PROC MIXED and MODEL statements are required. The MODEL statement must appear after the CLASS statement if CLASS statement is used. The CONTRAST, ESTIMATE, LSMEANS, RANDOM and REPEATED statement must follow the MODEL statement. CONTRAST and ESTIMATE statements must follow RANDOM statement if the RANDOM is used.A detailed description of all functions and options of each PROC MIXED statement is given inSAS/STAT Software Changes and Enhancements through Release 6.11 and SAS/STAT Software Changes and Enhancements for Release 6.12, SAS Institute Inc. (1996). The following is a short summary of selected, most often used, MIXED procedure statements.PROC MIXED <options>;Selected options:DATA= SAS data setNames SAS data set to be used by PROC MIXED. The default is the most recently created data set. METHOD=REMLMETHOD=MLMETHOD=MIVQUE0Specifies the estimation method. See Section 1 for a brief description of the methods and references. REML is the default method.COVTESTPrints asymptotic standard errors and Wald Z-test for variance-covariance structure parameter estimates. For example, if a random effect A is included in the model, then the estimator of the variance of A will be printed together with the Wald test of the hypothesis that the variance of A is 0.The COVTEST option is specified after Proc mixed and before semicolon;. For example,Proc mixed data=mydata method=reml covtest;CLASS variables;Lists classification variables (categorical independent variables in the model). For example:proc mixed data=mydata covtest;Class group gender agecat;MODEL dependent = fixed effects </options>;The model statement names a single dependent variable and the fixed effects, that is independent variables that are not random. An intercept is included in the model by default. The NOINT option can be used to remove the intercept.NOTE: Even though PROC MIXED allows only for one dependent variable in the model statement, it is possible to use it to model, for example, multivariate repeated measures. In such case, the data set has to be properly prepared and should contain a variable indicating the measurement type. The correlation between observations on the same unit has to be modeled properly with the REPEATED statement. For example, suppose your observed data consist of heights and weights of children measured over several successive years. Your input data set should then contain variables similar to the following:Y, all of the heights and weights, with a separate observation (line in the data file) for eachVAR, indicating whether the measurement is a height or a weightYEAR, indicating the year of measurementCHILD, indicating the child on which the measurement was taken.Selected Options of the model statement:CHISQ, request χ2 – tests (Wald tests) be performed for all fixed effects in addition to the F-tests. DDFM=RESIDUALDDFM=CONTAINDDFM=BETWITHNDDFM=SATTERTH,The DDFM= options specifies the method for computing the denominator degrees of freedom for the tests of fixed effects. DDFM=SATTERTH will result in the Satterthwaite approximation for the denominator degrees of freedom. For balanced designs with random effects it will produce the same test results as RANDOM …/ TEST option in PROC GLM (if the default METHOD=REML is used in proc mixed).P, requests that the predicted values be printed.RANDOM random effects </options>;The RANDOM statement defines the random effects in the model. It can be used to specify traditional variance components (independent random effects with different variances) or to list correlated random effects and specify a correlation structure for them with the TYPE=covariance-structure option. A variety of structures are available (see references 5 and 6), most often used are either TYPE=VC, a variance components correlation structure or TYPE=UN, an unstructured, that is, arbitrary covariance matrix. TYPE=VC is the default structure. In the following example, the effect of subject is random.Proc mixed data=one method=reml covtest;Class gender treat subject;Model y=gender treat gender*treat /ddfm=satterth;Random subject(gender);Run;In the next example there are two random effects specified (besides the error term) and it is assumed that they are correlated.Intercept and the slope coefficient in the regression equation have fixed and random parts which are assumed to be correlated. The model is:yij = a0 +aj + b0*time + bj*time + eij, where yij is observation i for person j.The random effects, aj, bj and eij, are asumed to have normal distributions with mean zero and different variances and it is also assumed that aj and bj are correlated.Proc mixed data=one method=reml covtest;Class person;Model y=time /solution;Random intercept time /type=un subject=person;Run;REPEATED repeated effects / options;The repeated statement is used in PROC MIXED to specify the covariance structure of the error term. The repeated effect has to be categorical and has to appear in the class statement and the data has to be sorted accordingly. For example, suppose that for each subject a measurement was taken at five equally spaced time points. The time is the repeated effect and the data has to be sorted by subject and time within each subject. If time is also used as a continuous independent variable in the model then a new variable, say t, identical to time has to be defined and t should be used in the class and repeated statements. For example:Data one;Set one;T=time;Run;Proc sort data=one;By group id t;Run;Proc mixed data=one covtest;Class t group id;Model y=group time group*time;Repeated t /type=ar(1) subject=id;Run;The option TYPE in the REPEATED statement specifies the type of the error correlation structure. The one specified in the above example is the first-order autoregressive correlation. The subject option is needed to identify observations that are correlated. Observations within the same subject are correlated with the type of correlation specified in TYPE, observations from different subjects are independent.The TYPE option allows for many types of correlation structures. Most commonly used are autocorrelation, compound symmetry, Huynh-Feldt, Toeplitz, variance components, unstructured and spatial. For the complete list and examples, see references (7) and (8).CONTRAST ‘label’ fixed-effect values | random-effect values / options;ESTIMATE ‘label’ fixed-effect values | random-effect values / options;The CONTRAST statement is used when there is need for custom hypothesis tests, the ESTIMATE statement, when there is need for custom estimates. Although they were extended in PROC MIXED to include random effects, their use is very similar to the CONTRAST and ESTIMATE statement in PROC GLM.LABEL is required for every contrast or estimate statement. It identifies the contrast or estimated parameter on the output. It can not be longer than 20 characters.FIXED-EFFECT is the name of an effect appearing in the MODEL statement.RANDOM-EFFECT is the name of an effect appearing in the RANDOM statement.VALUES are the coefficients of the contrast to be tested or the parameter to be estimated.For example, suppose that we want to test if there is a significant effect of treat in group 2, where treat has three levels and group four levels. We also want to estimate the mean for treat 1 in group 2, the mean for treat 2 in group 2 and the difference between these two means. We will need the following CONTRAST and ESTIMATE statements to obtain these results.Proc mixed data=one method=reml covtest;Class group treat subject;Model y=group treat group*treat /ddfm=satterth;Random subject(group);Contrast ‘treat in group 2’Treat 1 –1 0 group*treat 0 0 0 1 –1 0 0 0 0 0 0 0,Treat 0 1 –1 group*treat 0 0 0 0 1 –1 0 0 0 0 0 0;Estimate ‘treat1 group2 mean’ intercept 1 group 0 1 0 0 treat 1 0 0group*treat 0 0 0 1 0 0 0 0 0 0 0 0;Estimate ‘treat2 group2 mean’ intercept 1 group 0 1 0 0 treat 0 1 0Group*treat 0 0 0 0 1 0 0 0 0 0 0 0;Estimate ‘mean diff t1g2-t2g2’ Treat 1 –1 0 group*treat 0 0 0 1 –1 0 0 0 0 0 0 0;Run;LSMEANS fixed-effects / options;LSMEANS computes the least squares means of fixed effects. The ADJUST option requests a multiplecomparison adjustment to the p-values for pair-wise comparisons of means. The following adjustments are available: BON (Bonferroni), DUNNET, SCHEFFE, SIDAK, SIMULATE, SMM|GT2 and TUKEY. The ADJUST option results in all possible pair-wise comparisons. If comparisons with a control level are only needed then in addition to ADJUST option, PDIFF=control should be used. The SLICE option allows to test the significance of one effect at each level of another effect.For example, suppose that we want to compute the least squares means for group*treat and do pair-wise comparisons with the control being group 1 and treat 1. We also want to test for the significance of the treat effect within each group level using the SLICE option..Proc mixed data=one method=reml covtest;Class group treat subject;Model y=group treat group*treat /ddfm=satterth;Random subject(group);lsmeans group*treat /adjust=bon pdiff=control('1' '1') slice=group;Run;MAKE 'table' OUT= SAS-data-set < options >;The MAKE statement converts any table produced by PROC MIXED into a sas data set. NOPRINT option can be used to prevent printing the requested table. Only requested or default output can be converted into a sas data set. Hence, in particular, the P option has to be used in the model statement to produce a data set with predicted values, and the LSMEANS statement has to be included to output least squares means. For example,Proc mixed data=one method=reml covtest;Class group treat subject;Model y=group treat group*treat /ddfm=satterth p;Random subject(group);lsmeans group*treat /adjust=bon pdiff=control('1' '1') slice=group;make ‘LSMeans’ out=gtmeans;make ‘predicted’ out=pred noprint;Run;Proc print data=gtmeans;Proc print data=pred;Run;ReferencesStatistics Books:1. Searle, Shayle R. (1987). Linear Models For Unbalanced Data, John Wiley & Sons.2. Searle, Shayle R. (1971). Linear Models, John Wiley & Sons.3. Searle, S.R., Casella, G., and McCulloch, C.E. (1992), Variance Components. John Wiley&Sons.4. Verbeke, G., Molenberghs, G. (Editors) (1997), Linear Mixed Models in Practice. A SAS-Oriented Approach. Springer-VerlagSAS Institute Books:5. Littell, Ramon C., Milliken, George A., Stroup, Walter W., Wolfinger, Russell D. (1996). SAS System For Mixed Models, SAS Institute Inc.6. SAS Institute Course Notes (1996). Advanced General Linear Models with an Emphasis on Mixed Models, SAS Institute Inc.7. SAS/STAT Software Changes and Enhancements through Release 6.11, SAS Institute Inc. 1996.8. SAS/STAT Software Changes and Enhancements for Release 6.12, SAS Institute Inc. 1996.3. Examples and comparisons of the results from PROC MIXED and PROC GLM. Example1. Fixed effect model, balanced data.In this example, 36 subjects are randomly assigned to 12 group – treatment combinations, 3 to each combination. There are three treatments and four groups. In the following program, factor treat with 3 levels is the effect of the treatment and factor group with 4 levels is the effect of the group.As you can see below, the results from both procedures are identical.Program:options ls=76;data one;input y group treat subject;cards;22 1 1 123 1 1 225 1 1 317 1 2 418 1 2 523 1 2 612 1 3 716 1 3 814 1 3 98 2 1 109 2 1 1110 2 1 1216 2 2 1317 2 2 1420 2 2 1529 2 3 1630 2 3 1736 2 3 183 3 1 197 3 1 205 3 1 211 32 222 3 2 231 32 244 3 3 257 3 3 268 3 3 2711 4 1 2815 4 1 298 4 1 3034 4 2 3137 4 2 3233 4 2 3327 4 3 3428 4 3 3524 4 3 36;run;Proc mixed data=one method=reml;Class group treat;Model y=group treat group*treat;lsmeans group*treat /adjust=bon pdiff=control('1' '1') slice=group;Contrast 'treat in group 2'Treat 1 -1 0 group*treat 0 0 0 1 -1 0 0 0 0 0 0 0,Treat 0 1 -1 group*treat 0 0 0 0 1 -1 0 0 0 0 0 0;Estimate 'treat1 group2 mean' intercept 1 group 0 1 0 0 treat 1 0 0group*treat 0 0 0 1 0 0 0 0 0 0 0 0;Estimate 'treat2 group2 mean' intercept 1 group 0 1 0 0 treat 0 1 0Group*treat 0 0 0 0 1 0 0 0 0 0 0 0;Estimate 'mean diff t1g2-t2g2' Treat 1 -1 0 group*treat 0 0 0 1 -1 0 0 0 0 0 0 0; Run;proc GLM data=one;class group treat;Model y=group treat group*treat;lsmeans group*treat /adjust=bon pdiff=control('1' '1') slice=group;Contrast 'treat in group 2'Treat 1 -1 0 group*treat 0 0 0 1 -1 0 0 0 0 0 0 0,Treat 0 1 -1 group*treat 0 0 0 0 1 -1 0 0 0 0 0 0;Estimate 'treat1 group2 mean' intercept 1 group 0 1 0 0 treat 1 0 0group*treat 0 0 0 1 0 0 0 0 0 0 0 0;Estimate 'treat2 group2 mean' intercept 1 group 0 1 0 0 treat 0 1 0Group*treat 0 0 0 0 1 0 0 0 0 0 0 0;Estimate 'mean diff t1g2-t2g2' Treat 1 -1 0 group*treat 0 0 0 1 -1 0 0 0 0 0 0 0; Run;Results:The MIXED ProcedureGROUP 4 1 2 3 4TREAT 3 1 2 3Tests of Fixed EffectsSource NDF DDF Type III F Pr > FGROUP 3 24 121.60 0.0001TREAT 2 24 34.11 0.0001GROUP*TREAT 6 24 43.04 0.0001ESTIMATE Statement ResultsParameter Estimate Std Error DF t Pr > |t|treat1 group2 mean 9.00000000 1.35400640 24 6.65 0.0001treat2 group2 mean 17.66666667 1.35400640 24 13.05 0.0001mean diff t1g2-t2g2 -8.66666667 1.91485422 24 -4.53 0.0001CONTRAST Statement ResultsSource NDF DDF F Pr > Ftreat in group 2 2 24 71.35 0.0001Least Squares MeansEffect GROUP TREAT LSMEAN Std ErrorGROUP*TREAT 1 1 23.33333333 1.35400640GROUP*TREAT 1 2 19.33333333 1.35400640GROUP*TREAT 1 3 14.00000000 1.35400640GROUP*TREAT 2 1 9.00000000 1.35400640GROUP*TREAT 2 2 17.66666667 1.35400640GROUP*TREAT 2 3 31.66666667 1.35400640GROUP*TREAT 3 1 5.00000000 1.35400640GROUP*TREAT 3 2 1.33333333 1.35400640GROUP*TREAT 3 3 6.33333333 1.35400640GROUP*TREAT 4 1 11.33333333 1.35400640GROUP*TREAT 4 2 34.66666667 1.35400640GROUP*TREAT 4 3 26.33333333 1.35400640Differences of Least Squares MeansEffect GROUP TREAT GROUP _TREAT Difference Std Error DF GROUP*TREAT 1 2 1 1 -4.00000000 1.91485422 24 GROUP*TREAT 1 3 1 1 -9.33333333 1.91485422 24 GROUP*TREAT 2 1 1 1 -14.33333333 1.91485422 24 GROUP*TREAT 2 2 1 1 -5.66666667 1.91485422 24 GROUP*TREAT 2 3 1 1 8.33333333 1.91485422 24 GROUP*TREAT 3 1 1 1 -18.33333333 1.91485422 24 GROUP*TREAT 3 2 1 1 -22.00000000 1.91485422 24 GROUP*TREAT 3 3 1 1 -17.00000000 1.91485422 24 GROUP*TREAT 4 1 1 1 -12.00000000 1.91485422 24 GROUP*TREAT 4 2 1 1 11.33333333 1.91485422 24 GROUP*TREAT 4 3 1 1 3.00000000 1.91485422 24Differences of Least Squares Meanst Pr > |t| Adjustment Adj P-2.09 0.0475 Bonferroni 0.5224-4.87 0.0001 Bonferroni 0.0006-7.49 0.0001 Bonferroni 0.0000-2.96 0.0068 Bonferroni 0.07524.35 0.0002 Bonferroni 0.0024-9.57 0.0001 Bonferroni 0.0000-11.49 0.0001 Bonferroni 0.0000-8.88 0.0001 Bonferroni 0.0000-6.27 0.0001 Bonferroni 0.00005.92 0.0001 Bonferroni 0.00001.57 0.1303 Bonferroni 1.0000Tests of Effect SlicesEffect GROUP NDF DDF F Pr > FGROUP*TREAT 1 2 24 11.96 0.0002GROUP*TREAT 2 2 24 71.35 0.0001GROUP*TREAT 3 2 24 3.66 0.0411GROUP*TREAT 4 2 24 76.26 0.0001General Linear Models ProcedureClass Level InformationGROUP 4 1 2 3 4TREAT 3 1 2 3General Linear Models ProcedureDependent Variable: YSum of MeanSource DF Squares Square F Value Pr > F Model 11 3802.00000 345.63636 62.84 0.0001 Error 24 132.00000 5.50000Corrected Total 35 3934.00000R-Square C.V. Root MSE Y Mean0.966446 14.07125 2.34521 16.6667Source DF Type III SS Mean Square F Value Pr > F GROUP 3 2006.44444 668.81481 121.60 0.0001 TREAT 2 375.16667 187.58333 34.11 0.0001 GROUP*TREAT 6 1420.38889 236.73148 43.04 0.0001General Linear Models ProcedureLeast Squares MeansAdjustment for multiple comparisons: BonferroniGROUP TREAT Y Pr > |T| H0:LSMEAN LSMEAN=CONTROL1 1 23.33333331 2 19.3333333 0.52241 3 14.0000000 0.00062 1 9.0000000 0.00012 2 17.6666667 0.07522 3 31.6666667 0.00243 1 5.0000000 0.00013 2 1.3333333 0.00013 3 6.3333333 0.00014 1 11.3333333 0.00014 2 34.6666667 0.00014 3 26.3333333 1.0000GROUP*TREAT Effect Sliced by GROUP for YSum of MeanGROUP DF Squares Square F Value Pr > F1 2 131.555556 65.777778 11.9596 0.00022 2 784.888889 392.444444 71.3535 0.00013 2 40.222222 20.111111 3.6566 0.04114 2 838.888889 419.444444 76.2626 0.0001Dependent Variable: YContrast DF Contrast SS Mean Square F Value Pr > Ftreat in group 2 2 784.888889 392.444444 71.35 0.0001T for H0: Pr > |T| Std Error ofParameter Estimate Parameter=0 Estimatetreat1 group2 mean 9.0000000 6.65 0.0001 1.35400640treat2 group2 mean 17.6666667 13.05 0.0001 1.35400640mean diff t1g2-t2g2 -8.6666667 -4.53 0.0001 1.91485422Example 2. Mixed effect model, balanced data.In this example, 12 subjects are randomly assigned to 4 groups, 3 to each group. There are three observations for each subject corresponding to measurements taken at time 1, 2 and 3. In the following program, factor time with 3 levels is the effect of the time and factor group with 4 levels is the effect of the group.A mixed effect model with fixed effect of group and time and random effect of subject will be used to analyze the data. It is assumed that the effect of the subject has a normal distribution with mean 0 and variance sigmaS squared (it measures between subject variability). It is also assumed that the error term has a normal distribution with mean 0 and variance sigmaE squared (it measures within subject error) and the error and subject effects are not correlatedAs you can see below, the results of MIXED and GLM are not identical. The F and p-values for the tests are the same. Values from proc mixed have to be compared with the Tests of Hypotheses for MixedModel Analysis from proc GLM, not with the main, General Linear Model Procedure, ANOVA table. The values in the main ANOVA table in proc GLM are incorrect for this example; they are computed under the assumption that subject is a fixed effect. However, the standard error of the lsmeans and requested estimates are not the same for proc MIXED and proc GLM. The ones printed by proc MIXED are correct. Again, proc GLM computed the standard error assuming that the subject effect is fixed. Note that the standard error for the third estimate, the mean difference between time 1 and time 2 in group 2 is the same for both. This is because when you compute that difference, the effect of the subject cancels out.Also note that proc GLM results printed in the Test of Hypotheses table include the F-test for the significance of the subject effect. The test is not printed in proc Mixed. The corresponding table includes only the fixed effects. The estimates of the random effects, in this case sigmaS squared (variance of the subject effect) and sigmaE squared (variance of the error term) are printed in the table named Covariance Parameter Estimates. The test of significance is the Wald test. The estimates are consistent with the proc GLM results. The residual variance in proc MIXED is the same as MSS (mean sum of squares) for the error in proc GLM. The subject variance can be computed from the GLM Type III Expected Mean Square table.Type III Expected Mean SquareGROUP Var(Error) + 3 Var(SUBJECT(GROUP)) + Q(GROUP,GROUP*TIME)SUBJECT(GROUP) Var(Error) + 3 Var(SUBJECT(GROUP))TIME Var(Error) + Q(TIME,GROUP*TIME)GROUP*TIME Var(Error) + Q(GROUP*TIME)According to that table, MSS(subject)=var(error)+3*var(subject). Hence var(subject)=(MSS(subject) – var(error))/3. Since the expected mean of MSS(error)=var(error), we can use MSS(error) as the estimate of var(error) and replace var(error) with MSS(error) in the above formula. Thus,Var(subject)=(12.5278 – 1.9861)/3=3.5139,which is the same as the value printed in the proc MIXED Covariance Parameter Estimates table for the subject.Program:options ls=76;data one;input y group time subject;cards;22 1 1 123 1 1 225 1 1 317 1 2 118 1 2 223 1 2 312 1 3 116 1 3 214 1 3 38 2 1 49 2 1 510 2 1 616 2 2 417 2 2 520 2 2 629 2 3 430 2 3 536 2 3 63 3 1 77 3 1 85 3 1 91 32 72 3 2 81 32 94 3 3 77 3 3 88 3 3 911 4 1 1015 4 1 118 4 1 1234 4 2 1037 4 2 1133 4 2 1227 4 3 1028 4 3 1124 4 3 12;run;proc sort data=one;by group subject time;run;Proc mixed data=one method=reml covtest;Class group time subject;Model y=group time group*time / DDFM=SATTERTH;RANDOM SUBJECT(group);lsmeans group*time /adjust=bon pdiff=control('1' '1') slice=group;Contrast 'time in group 2'time 1 -1 0 group*time 0 0 0 1 -1 0 0 0 0 0 0 0,time 0 1 -1 group*time 0 0 0 0 1 -1 0 0 0 0 0 0;Estimate 'time1 group2 mean' intercept 1 group 0 1 0 0 time 1 0 0group*time 0 0 0 1 0 0 0 0 0 0 0 0;Estimate 'time2 group2 mean' intercept 1 group 0 1 0 0 time 0 1 0Group*time 0 0 0 0 1 0 0 0 0 0 0 0;Estimate 'mean diff t1g2-t2g2' time 1 -1 0 group*time 0 0 0 1 -1 0 0 0 0 0 0 0; Run;proc GLM data=one;class group time subject;。
python随机模块random的22种函数（小结）
python随机模块random的22种函数（⼩结）前⾔ 随机数可以⽤于数学，游戏，安全等领域中，还经常被嵌⼊到算法中，⽤以提⾼算法效率，并提⾼程序的安全性。
平时数据分析各种分布的数据构造也会⽤到。
random模块，⽤于⽣成伪随机数，之所以称之为伪随机数，是因为真正意义上的随机数（或者随机事件）在某次产⽣过程中是按照实验过程中表现的分布概率随机产⽣的，其结果是不可预测的，是不可见的。
⽽计算机中的随机函数是按照⼀定算法模拟产⽣的，对于正常随机⽽⾔，会出现某个事情出现多次的情况。
但是伪随机在事情触发前设定好，就是这个⼗个事件各发⽣⼀次，只不过顺序不同⽽已。
现在MP3的随机列表就是⽤的伪随机，把要播放的歌曲打乱顺序，⽣成⼀个随机列表⽽已，每个歌曲都播放⼀次。
真实随机的话，会有出现某⾸歌多放次的情况，歌曲基数越多，重放的概率越⼤。
注意：random()是不能直接访问的，需要导⼊ random 模块，然后通过 random 静态对象调⽤该⽅法。
import randomlist(dir(random))['BPF', 'LOG4','NV_MAGICCONST','RECIP_BPF','Random','SG_MAGICCONST','SystemRandom','TWOPI','betavariate','choice','choices','expovariate','gammavariate','gauss','getrandbits','getstate','lognormvariate','normalvariate','paretovariate','randint','random','randrange','sample','seed','setstate','shuffle','triangular','uniform','vonmisesvariate','weibullvariate']#加载所需要的包import randomimport matplotlib.pyplot as pltimport seaborn as snsrandom.random()描述：random.random() ⽤于⽣成⼀个0到1的随机符点数: 0 <= n < 1.0语法：random.random()#⽣成⼀个随机数random.random()0.7186311708109537#⽣成⼀个4位⼩数的随机列表[round(random.random(),4) for i in range(10)][0.1693, 0.4698, 0.5849, 0.6859, 0.2818, 0.216, 0.1976, 0.3171, 0.2522, 0.8012]#⽣成⼀串随机数for i in range(10):print(random.random())0.43860556392473480.43944378539770780.2318629636828330.64831689635533420.121065812558118550.70438749865313550.387295196584986230.64922561571703930.4634250509335640.2298431522075462random.choice()描述：从⾮空序列seq中随机选取⼀个元素。
逻辑回归中random_state作用-概述说明以及解释
逻辑回归中random_state作用-概述说明以及解释1.引言1.1 概述逻辑回归是一种常用的分类算法，广泛应用于机器学习和数据分析领域。
它被用于预测一个特征变量的取值对应的目标变量的概率。
与其他分类算法相比，逻辑回归具有简单、高效和可解释性强的特点。
在逻辑回归中，random_state是一个用于控制随机性的参数。
它用于设置随机数生成器的种子，以确保每次运行模型时得到的结果是可复现的。
由于逻辑回归模型中涉及到随机梯度下降等随机性的操作，设置random_state可以控制每次模型训练的随机状态，从而影响模型的性能表现。
设置random_state的作用主要有两个方面。
首先，它可以保证模型训练的可重复性。
对于相同的数据集和参数设置，如果random_state相同，那么每次运行模型时得到的结果将完全一样。
这在实验设计和模型比较时非常重要，可以确保结果的可靠性和一致性。
其次，random_state还可以用于避免模型过拟合。
在逻辑回归中，模型的参数会根据训练数据的随机抽样而变化。
通过设置random_state，我们可以固定模型参数的随机初始化过程，从而减轻模型过拟合的风险。
这对于小样本数据集尤为重要，可以提高模型的泛化能力并避免在训练集上出现过度拟合的情况。
总之，random_state在逻辑回归中具有重要的作用。
它可以保证模型训练的可重复性，并且有助于避免模型过拟合的问题。
在实际应用中，我们可以根据具体情况选择合适的random_state值，以获得稳定和准确的模型结果。
1.2 文章结构本文旨在探讨逻辑回归中的random_state 参数的作用。
文章内容分为引言、正文和结论三个部分。
引言部分首先对整篇文章进行概述，简要介绍逻辑回归模型和random_state 参数，并明确文章的目的。
正文部分包括两个章节，分别是逻辑回归的基本概念和random_state 的作用。
在逻辑回归的基本概念章节中，将介绍逻辑回归模型的原理、应用场景以及参数设置等方面的内容。
math.random()方法生成的随机整数_概述说明以及解释
math.random()方法生成的随机整数概述说明以及解释1. 引言1.1 概述在计算机编程中，随机数的生成对于许多应用程序来说是至关重要的。
而在JavaScript语言中，我们可以使用Math对象的random()方法来生成随机数。
本文将对这个方法进行全面的概述和解释。
1.2 目的本篇文章旨在介绍Math对象的random()方法以及通过该方法生成的随机整数。
我们将详细探讨该方法的使用注意事项、原理分析、优缺点分析，并与其他随机数生成方法进行比较。
通过深入了解这个方法，读者能够更好地理解它的特点和适用场景，并且能够在实际应用中做出明智的决策。
1.3 结构本文将按照以下结构展开对Math.random()方法生成随机整数的说明：第2部分：math.random()方法简介2.1 方法概述2.2 随机整数生成范围2.3 使用注意事项第3部分：随机整数生成原理分析3.1 伪随机性说明3.2 算法基础介绍3.3 实际应用举例第4部分：math.random()方法优缺点分析4.1 优势总结4.2 不足之处展示4.3 与其他随机数方法对比第5部分：结论与展望5.1 总结论述5.2 展望未来发展方向5.3 实际应用建议通过以上划分的章节，读者将能够全面了解math.random()方法生成的随机整数，并且可以根据自己的需求和实际情况做出合理的选择与应用。
2. math.random()方法简介2.1 方法概述math.random()是JavaScript中的一个用于生成随机数的函数。
它返回一个0到1之间的随机浮点数，包含0但不包含1。
2.2 随机整数生成范围尽管math.random()生成的是浮点数，我们可以利用一些技巧将其转换为整数。
例如，要生成0到9之间（包含0和9）的随机整数，我们可以使用以下代码：```Math.floor(Math.random() * 10)```其中Math.floor()函数会将参数向下取整，即去除小数部分，保留整数部分。
randomnumber函数
randomnumber函数randomnumber函数是一种常见的编程函数，可以生成一个指定范围内的随机数。
在计算机科学中，随机数起到了很重要的作用，它们被广泛应用于各种领域，包括游戏开发、密码学、模拟实验等等。
randomnumber函数的实现方法有很多种，下面我们将介绍其中一种常见的实现方法。
我们需要明确randomnumber函数的功能和参数。
该函数的功能是生成一个指定范围内的随机数，参数包括最小值和最大值。
例如，如果我们调用randomnumber(1, 10)，函数将会生成一个1到10之间的随机数。
接下来，我们可以通过使用编程语言来实现randomnumber函数。
以Python语言为例，可以使用random模块中的randint函数来实现。
下面是一个示例代码：```pythonimport randomdef randomnumber(min_value, max_value):return random.randint(min_value, max_value)```在这个示例代码中，我们首先导入了random模块，然后定义了randomnumber函数，并在函数内部使用了randint函数来生成随机数。
最后，我们通过return语句将生成的随机数返回。
使用randomnumber函数非常简单，只需要提供最小值和最大值作为参数即可。
下面是一个示例代码：```pythonresult = randomnumber(1, 10)print(result)```在这个示例代码中，我们调用了randomnumber函数，并将生成的随机数赋值给result变量，然后打印出来。
运行代码后，我们将会看到输出的随机数。
除了Python语言，其他编程语言也提供了类似的函数来生成随机数。
例如，在JavaScript语言中，可以使用Math对象的random方法来生成0到1之间的随机数，然后通过一些计算来将其转换为指定范围内的随机数。
random variable 的英文解释
random variable 的英文解释Random variables are an essential concept in probability theory and statistics, as they play a crucial role in modeling and analyzing uncertain phenomena. A random variable is a mathematical function that assigns a numerical value to each possible outcome of a random experiment. In other words, it is a variable that can take on different values with certain probabilities.The concept of a random variable is fundamental in many areas of study, including finance, engineering, biology, and social sciences, where researchers and analysts need to deal with uncertainty and make decisions based on probabilistic information. By understanding and working with random variables, we can gain insights into the behavior of complex systems, make more informed decisions, and better understand the world around us.One of the key characteristics of a random variable is its probability distribution, which describes the likelihood of the variable taking on different values. The probability distribution can be either discrete or continuous, depending on the nature of the random variable. Discrete random variables can only take on a finite or countable number of values, while continuous random variables can take onany value within a specified range.Discrete random variables are often used to model situations where the possible outcomes are distinct and countable, such as the number of heads in a series of coin flips or the number of defective items in a production process. In these cases, the probability distribution can be described by a probability mass function, which assigns a probability to each possible value of the random variable.Continuous random variables, on the other hand, are used to model situations where the possible outcomes are not discrete, such as the height of individuals in a population or the time it takes for a machine to break down. In these cases, the probability distribution can be described by a probability density function, which specifies the relative likelihood of the random variable taking on different values within a continuous range.One of the most important properties of random variables is their expected value, also known as the mean or average. The expected value represents the long-term average or typical value of the random variable, and it is calculated as the weighted average of all possible values, with the weights being the corresponding probabilities. The expected value is a crucial measure in decision-making, as it provides a way to quantify the central tendency of a random variable.Another important property of random variables is their variance, which measures the spread or dispersion of the values around the expected value. The variance reflects the degree of uncertainty or variability associated with the random variable, and it is calculated as the average of the squared deviations from the expected value. The square root of the variance, known as the standard deviation, is also a commonly used measure of variability.Random variables can also be classified based on their independence or dependence. Independent random variables are those whose values are not influenced by the values of other random variables, while dependent random variables are those whose values are related to the values of other random variables. Understanding the relationships between random variables is crucial in many applications, as it allows for more accurate modeling and better decision-making.In addition to these basic properties, random variables can also exhibit more complex characteristics, such as skewness (the asymmetry of the probability distribution) and kurtosis (the peakedness or "tailedness" of the distribution). These higher-order moments can provide additional insights into the behavior of the random variable and its potential impact on the system or process being studied.The concept of random variables is not only important in theoretical studies but also has numerous practical applications. In finance, for example, random variables are used to model stock prices, interest rates, and other financial variables, which are crucial for investment decisions and risk management. In engineering, random variables are used to model the reliability and performance of systems, such as the lifetime of electronic components or the strength of materials. In biology, random variables are used to model the genetic variations within a population or the spread of infectious diseases.In conclusion, random variables are a fundamental concept in probability theory and statistics, and they play a crucial role in modeling and analyzing uncertain phenomena. By understanding the properties and characteristics of random variables, researchers and analysts can make more informed decisions, gain deeper insights into complex systems, and better understand the world around us.。
randomnumber函数
randomnumber函数randomnumber函数是一种常见的编程函数，用于生成随机数。
随机数在计算机科学中具有广泛的应用，可以用于密码学、模拟实验、游戏开发等众多领域。
本文将介绍randomnumber函数的基本原理和应用场景，并探讨它对现代科技的重要性。
让我们来了解randomnumber函数的原理。
该函数的作用是生成一个在指定范围内的随机数。
这个范围可以是整数、小数或其他类型的数据。
randomnumber函数通过使用一种称为“伪随机数生成器”的算法来实现。
伪随机数生成器是一种基于确定性算法的随机数生成器，它使用一个称为“种子”的初始值来生成随机数序列。
在同一个种子的情况下，randomnumber函数将生成相同的随机数序列。
randomnumber函数的应用非常广泛。
在密码学中，随机数被用作加密算法的重要组成部分。
通过生成随机数作为密钥或初始化向量，可以增加加密算法的安全性。
在模拟实验中，随机数可以用来模拟真实世界的随机事件，从而帮助科学家进行各种实验研究。
在游戏开发中，随机数可以用来生成游戏中的随机事件和随机数值，增加游戏的趣味性和挑战性。
除了上述应用，随机数还可以用于数据分析和统计学。
在统计学中，随机数可以作为样本数据的生成方式，用于进行统计推断和假设检验。
在数据分析中，随机数可以用来生成模拟数据，进行模型验证和预测。
然而，尽管randomnumber函数在各个领域有着广泛的应用，但它也存在一些问题和注意事项。
首先，由于randomnumber函数生成的随机数是伪随机数，而不是真正的随机数，因此在某些情况下可能不够随机。
为了解决这个问题，可以使用更复杂的随机数生成算法或者使用外部的随机数源。
其次，如果使用相同的种子值，randomnumber函数将生成相同的随机数序列。
为了确保随机性，应该使用不同的种子值或者使用系统时间作为种子。
随机数的生成也可能受到计算机硬件和操作系统的限制。
c中random的用法
c中random的用法下面小编就跟你们详细介绍下c中random的用法的用法，希望对你们有用。
c中random的用法的用法如下：random函数不是ANSI C标准，不能在gcc,vc等编译器下编译通过。
但在C语言中int random(num)可以这样使用，它返回的是0至num-1的一个随机数。
可改用C++下的rand函数来实现。
rand()%n 范围 0~n-1rand()主要是实现产生随机数，其他我们在这里可以无视他显然任意一个数 rand()%n 范围显然是 0~n-1;那么如何产生 n~m的数呢？一样的我们只要对rand()进行一些符号操作就行了；n+rand()%(m-n+1); 这样就可以了这样我们就只有种子和浮点数的没有分析了，下面来说rand()的用法，浮点数的放在最后面讲：一般在用这个之前都要初始化一个种子，但是你不写的话，系统会给你一个默认的种子，下面是我们自己输入种子的代码；[cpp] view plain copy01.int seed;02.03.scanf ("%d",&seed);04.05.srand(seed);06.07.cout<<rand()<<endl;[cpp] view plain copy01.#include <stdio.h>02.#include <stdlib.h>03.#include <time.h>04.int main()05.{06. int arr[15];07. //srand(time(NULL));08. int seed;09. while(1){10. scanf("%d",&seed);11. srand(seed);12. for (int i=0; i<15; i++)13. printf ("%d\t",rand()%10);14. printf ("\n");15. }16. return 0;17.}经过下图的比较发现，每一个种子都是保持着这个状态的随机变量值，会存在系统里面；因此，我们要对这个初始化种子保持着时刻不同；也就是说我们还是用 srand(time(NULL));比较好用如下代码比较合适：[cpp] view plain copy01.#include <stdio.h>02.#include <stdlib.h>03.#include <time.h>04.int main()05.{06. //int arr[15];07. srand(time(NULL));08. for (int i=0; i<15; i++)09. printf ("%d\t",rand()%10);10. printf ("\n");11. while (1);12. return 0;13.}好了，我们现在讲下最后一点---------浮点数的随机产生rand()%n =========== 0~n-1 那么我们再除以 n 就行了可以表示为： (rand()%n)/(n*1.0) //这里注意下隐式转换低------>高下面给出一个范例：[cpp] view plain copy01.#include <stdio.h>02.#include <stdlib.h>03.#include <time.h>04.int main()05.{06. int arr[15];07. //srand(time(NULL));08. int seed;09. while(1){10. scanf("%d",&seed);11. srand(seed);12. for (int i=0; i<15; i++)13. printf ("%lf\t",(rand()%10)/10.0);14. printf ("\n");15. }16. return 0;17.}。
Random生成随机数
Random⽣成随机数Random类 (java.util)Random类中实现的随机算法是伪随机，也就是有规则的随机。
在进⾏随机时，随机算法的起源数字称为种⼦数(seed)，在种⼦数的基础上进⾏⼀定的变换，从⽽产⽣需要的随机数字。
相同种⼦数的Random对象，相同次数⽣成的随机数字是完全相同的。
也就是说，两个种⼦数相同的Random对象，第⼀次⽣成的随机数字完全相同，第⼆次⽣成的随机数字也完全相同。
这点在⽣成多个随机数字时需要特别注意。
下⾯介绍⼀下Random类的使⽤，以及如何⽣成指定区间的随机数组以及实现程序中要求的⼏率。
1、Random对象的⽣成Random类包含两个构造⽅法，下⾯依次进⾏介绍：a、public Random()该构造⽅法使⽤⼀个和当前系统时间对应的相对时间有关的数字作为种⼦数，然后使⽤这个种⼦数构造Random对象。
b、public Random(long seed)该构造⽅法可以通过制定⼀个种⼦数进⾏创建。
⽰例代码：复制代码代码如下:Random r = new Random();Random r1 = new Random(10);再次强调：种⼦数只是随机算法的起源数字，和⽣成的随机数字的区间⽆关。
2、Random类中的常⽤⽅法Random类中的⽅法⽐较简单，每个⽅法的功能也很容易理解。
需要说明的是，Random类中各⽅法⽣成的随机数字都是均匀分布的，也就是说区间内部的数字⽣成的⼏率是均等的。
下⾯对这些⽅法做⼀下基本的介绍：a、public boolean nextBoolean()该⽅法的作⽤是⽣成⼀个随机的boolean值，⽣成true和false的值⼏率相等，也就是都是50%的⼏率。
b、public double nextDouble()该⽅法的作⽤是⽣成⼀个随机的double值，数值介于[0,1.0)之间。
c、public int nextInt()该⽅法的作⽤是⽣成⼀个随机的int值，该值介于int的区间，也就是-231到231-1之间。
举例说明的英文作文模版
举例说明的英文作文模版Title: Unleashing Creativity: A Random Journey with ChatGPT。
1. (Rhetorical Question)。
Imagine this, my dear friend, have you ever pondered the unpredictable nature of artistic inspiration? It's like a sudden storm, unpredictable and full of surprises, isn't it? In the realm of language, my existence, ChatGPT, isthat very tempest, ready to spark your imagination.2. (Metaphor)。
Just like a kaleidoscope, I am a collection of words, each one a colorful piece, rearranged to create a unique story. My function? To challenge the conventional, to dance around the boundaries of grammar, and to challenge your understanding of what a response can be.3. (Anecdote)。
Remember that time you stumbled upon a random quote? It was like finding a hidden treasure, wasn't it? Well, that's how I operate. I'm not bound by rules, but a free spirit, delivering unexpected insights with every interaction.4. (Personal Experience)。
Common Words (random)
word meaning examplemercurial (adjective): (of a person) prone tounexpected and unpredictablechanges in moodThe fact that Ella's moods were as mercurial as theweather was problematic for her relationships--itdidn't help that she lived in Chicago.derivative (adjective): (or a creative product,e.g. music, writing, etc.) not originalbut drawing on thework of another person Because the movies wereutterly derivative of other popular movies, they didwell at the box office. This word has other definitionsbut this is the most important one for the GREignominious (adjective): (used of conduct orcharacter) deserving or bringingdisgrace or shameSince the politician preached ethics and morality, histexting of revealing photographs was ignominious,bringing shame on both himself and his party.Common Wordsunequivocal (adjective): admitting of no doubtor misunderstanding; having onlyone meaning orinterpretation and leading to only one conclusion ThePresident's first statement on the subject was vagueand open to competing interpretations, so when hespoke to Congress about the same subject later, he wascafeful to make his position completely unequivocal.forthcoming(adjective): at ease in talking toothers As a husband, Larry was not forthcoming: if Jill didn't demand to know details, Larry would never share them with her.obsequious (adjective): attentive in aningratiating or servile manner;attempting to win favor frominfluential people by flattery The obsequious waiterdid not give the couple a moment's peace all throughthe meal, constantly returning to their table to refilltheir water glasses and to tell them what a handsomepair they made.forthcoming(adjective): available when requiredor as promised The President announced that the senators were about to reach a compromise, and that he was eager to read the forthcoming details of the bill.economical(adjective): avoiding waste, efficient Journalists favor an economical style of writing, inwhich no unnecessary words are used and everysentence is as short as possible.arbitrary(adjective): based on a random,groundless decision One of the arbitrary decrees in place during the emperor's rule is that all citizens pay him weekly homage at his palace. This word has other definitions but this is the most important one for the GREspecious(adjective): based on pretense;deceptively pleasing Almost every image on TV is specious and not to be trusted.impertinent(adjective): being disrespectful;improperly forward or bold Dexter, distraught over losing his pet dachshund, Madeline, found the police officer's questions impertinent--after all, he thought, did she have to pry into such details as to what Madeline's favorite snack was?tantamount(adjective): being essentially equalto something In many situations, remaining silent is tantamount to admitting guilt, so speak to prove your innocence.rudimentary (adjective): being in the earlieststages of development; being orinvolving basic facts orprinciples I would love to be able to present a fullypolished proposal to the board, but right now, ourplans for the product are still in the most rudimentarystages.apocryphal(adjective): being of questionableauthenticity The web is notorious for sandwiching apocryphal stories between actual news.belligerent(adjective): characteristic of oneeager to fight Tom said that he was arguing the matter purely for philosophical reasons, but his belligerent tone indicated an underlying anger about the issue.rustic (adjective): characteristic of rurallife; awkwardly simple andprovincialThe vacation cabin had no electricity and no indoorplumbing, but despite these inconveniences, Nigeladored its rustic charm.provincial (adjective): characteristic of the alimited perspective; not fashionableor sophisticatedMaggie's enthusiasm about her high school teamsseemed provincial to her college classmates, all ofwhom were following a nationally ranked college team.scrupulous(adjective): characterized byextreme care and great effort Because of his scrupulous nature, Mary put him in charge of numbering and cataloging the entire collection of rare stamps.decorous(adjective): characterized by goodtaste in manners and conduct Sally's parties are decorous affairs, and instead of the usual beer and music, there is tea and intellectual conversation.precocious (adjective): characterized by orcharacteristic of exceptionally earlydevelopment or maturity(especially in mental aptitude) Though only sevenyears old, she was a precocious chess prodigy, able tobeat players twice her age.gossamer(adjective): characterized byunusual lightness and delicacy The gossamer wings of a butterfly, which allow it to fly, are also a curse, so delicate that they are often damaged.winsome(adjective): charming in a childlikeor naive way She was winsome by nature, and many people were drawn to this free and playful spirit.artful(adjective): clever in a cunning way Bernie Madoff's artful Ponzi scheme stole billions ofdollars from investors and is considered the largestfinancial fraud in U.S. history.maladroit(adjective): clumsy As a child she was quite maladroit, but as an adult, she has become an adept dancer. This word has other definitions but this is the most important one for the GREinvolved(adjective): complicated, anddifficult to comprehend The physics lecture became so involved that the undergraduate's eyes glazed over.eclectic(adjective): comprised of a variety ofstyles Joey was known for his eclectic tastes in music, one moment dancing to disco the next "air conducting" along to Beethoven's 9th symphony.aesthetic(adjective): concerned with theappreciation of beauty The director, not known for his aesthetic sensibilities, decided not to use costumes at all, and put on the play in everyday clothing.esoteric (adjective): confined to andunderstandable by only anenlightened inner circleMap collecting is an esoteric hobby to most, but togeography geeks it is a highly enjoyable pasttime.equivocal(adjective): confusing or ambiguous The findings of the study were equivocal--the tworesearchers had different opinions on what the resultssignified.vociferous (adjective): conspicuously andoffensively loud; given to vehementoutcryIn giving Marcia a particular vociferous response, Paulcaused people at every other table in the restaurant toturn around an look at them angrily.discrete(adjective): constituting a separateentity or part What was once known as Czechoslovakia has since split into two discrete, independent nations.treacherous(adjective): dangerously unstableand unpredictable The bridge built from twine and vine is treacherous to walk across, and so I think I will stay put right here.iconoclastic(adjective): defying tradition orconvention Jackson Pollack was an iconoclastic artist, totally breaking with tradition by splashing paint on a blank canvas.arduous (adjective): demanding considerablemental effort and skill; testingpowers of enduranceIn order to deal with the arduous cross-countryjourney, truck drivers often survive on a string ofcaffeinated drinks, staying awake for up to 30 hours ata time.stringent(adjective): demanding strictattention to rules and procedures Most of the students disliked the teacher because of his stringent homework policy, but many students would later thank him for demanding so much from them.implausible(adjective): describing a statementthat is not believable The teacher found it implausible that the student was late to school because he had been kidnapped by outlaws on horseback.capricious (adjective): determined by chanceor impulse or whim rather than bynecessity or reasonNearly every month our capricious CEO had a newplan to turn the company around, and none of themworked because we never gave them the time theyneeded to succeed.recondite (adjective): difficult to penetrate;incomprehensible to one ofordinary understanding orknowledge I found Ulysses recondite and neverfinished the book, waiting instead to read it withsomeone else so we could penetrate its meaningtogether.abstruse(adjective): difficult to understand;incomprehensible Physics textbooks can seem so abstruse to the uninitiated that readers feel as though they are looking at hieroglyphics.disaffected(adjective): discontented as towardauthority After watching his superior take rations from the soliders, he quickly became disaffected and rebeled.ignoble(adjective): dishonorable In the 1920s, the World Series was rigged--an ignobleact which baseball took decades to recover from.hegemony(adjective): dominance over acertain area Until the Spanish Armada was defeated in 1587, Spain had hegemony over the seas, controlling waters stretching as far as the Americas.precipitous(adjective): done with very greathaste and without due deliberation He was expecting a precipitous rise in the value of a "hot" tech stock, so he was disappointed when it only inched up a dollar or two each day.petulant(adjective): easily irritated orannoyed When Ed first met Ruth, he didn't realize she was so petulant, but now that they are three months into their relationship, Ed feels a day doesn't go by in which she isn't whining about some minor issue.amenable(adjective): easily persuaded Even though she did not like the outdoors, Shirley wasgenerally amenable and so her brother was able topersuade her to go camping.poignant(adjective): emotionally touching After the Montagues and Capulets discover the dead bodies of Romeo and Juliet, in the play's most poignant moment, the two griefstricken familes agree to end their feud once and for all. This word has other definitions but this is the most important one for the GREedifying (adjective): enlightening or upliftingso as to encourage intellectual ormoral improvementI recently read an article in the Times about whethergood literature is edifying or not; specifically, doesreading more make a person more moral.pernicious (adjective): exceedingly harmful;working or spreading in a hiddenand injurious wayThe most successful viruses are pernicious: an infectedperson may feel perfectly healthy for several monthswhile incubating and spreading the virus.avaricious(adjective): excessively greedy Since avaricious desire is similar to gluttony or lust--sins of excess--it was listed as one of the seven deadlysins by the Catholic church.artful(adjective): exhibiting artistic skill Picasso is generally considered the most artfulmember of the Cubist movement.dictatorial (adjective): expectingunquestioning obedience;characteristic of an absolute rulerThe coach was dictatorial in his approach: no playerscould ever argue or question his approach.pejorative(adjective): expressing disapproval(usu. refers to a term) Most psychologists object to the pejorative term "shrink", believing that they expand the human mind, not limit it. This word has other definitions but this is the most important one for the GREparsimonious(adjective): extremely frugal;miserly Katie is so parsimonious that she only buys a pair of socks if all of her other socks have holes in them.ravenous (adjective): extremely hungry;devouring or craving food in greatquantitiesJohn didn't each much at all during the week he hadthe flu, so now that he is regaining his health, it's notsurpring that he has a ravenous appetite.auspicious(adjective): favorable, the oppositeof sinister Despite an auspicious beginning, Mike's road trip became a series of mishaps, and he was soon stranded and penniless, leaning against his wrecked automobile.intrepid(adjective): fearless Captain Ahab was an intrepid captain whose recklessand fearless style ultimate leads to his downfall.reverent(adjective): feeling or showingprofound respect or veneration The professor could speak objectively about the other composers, but he always lectured about Brahms with a particularly reverent air, unable to offer a single criticism of his compositions.staunch(adjective): firm and dependableespecially in loyalty No longer a staunch supporter of the movement, Todd now will openly question whether its goals are worthwhile.entrenched(adjective): fixed firmly or securely By the time we reach 60-years old, most of our habitsare so entrenched that it is difficult for us to change.quotidian(adjective): found in the ordinarycourse of events Phil gets so involved thinking about Aristotle's arguments that he totally forgets quotidian concerns, such as exercising and eating regularly.impartial(adjective): free from undue bias orpreconceived opinions The judge was not impartial since he had been bribed by the witness's family.guileless(adjective): free of deceit At first I thought my niece was guileless, but I thenfound myself buying her ice cream every time wepassed a shop.jubilant (adjective): full of high-spiriteddelight because of triumph orsuccessMy hardwork paid off, and I was jubilant to receive aperfect score on the GRE.jovial(adjective): full of or showing high-spirited merriment The political candidate and his supporters were jovial once it was clear that she had won.garrulous(adjective): full of trivialconversation Lynne was garrulous: once, she had a fifteen minute conversation with a stranger before she realized the woman didn't speak English.pragmatic (adjective): guided by practicalexperience and observation ratherthan theoryRather than make a philosophical appeal to theCongressmen, the Speaker decided to take a far morepragmatic approach, making small side-deals thatwould add votes to his bill.inveterate(adjective): habitual He is an inveterate smoker and has told his family andfriends that there is no way he will ever quit. querulous(adjective): habitually complaining The querulous old woman was begining to wear downeven the happier members of the staff with herceaseless complaining.taciturn(adjective): habitually reserved anduncommunicative While the CEO enthusiastically shares his plans and agenda with all who will listen, the CFO is far more taciturn, rarely revealing his perspective.deleterious(adjective): harmful to living things The BP oil spill in the Gulf of Mexico was deleteriousto the fishing industry in the southern states.innocuous(adjective): harmless and doesn"tproduce any ill effects Everyone found Nancy's banter innocuous--except for Mike, who felt like she was intentionally picking on him.austere(adjective): harsh in manner oftemperament The principal of my elementary school was a cold, austere woman; I could never understand why she chose to work with children.acerbic(adjective): harsh in tone Most movie critics are acerbic towards summerblockbusters, often referring to them as garbage.scrupulous(adjective): having a sense of rightand wrong; principled Everyone trusted what he said and followed his example because he was scrupulous and honest.incisive (adjective): having ordemonstrating ability to recognizeor draw fine distinctionsThe lawyer had an incisive mind, able in a flash todissect a hopelessly tangled issue and isolate theessential laws at play.haughty (adjective): having or showingarrogant superiority to and disdainof those one views asunworthy The haughty manager didn't believe that anyof his subordinates could ever have an insight asbrilliant his own.erudite(adjective): having or showingprofound knowledge Before the Internet, the library was typically were you would find erudite readers.dogmatic (adjective): highly opinionated, notaccepting that your belief may notbe correctBryan is dogmatic in his belief that the earth is flat,claiming that all pictures of a spherical earth arecomputer generated.inimical (adjective): hostile (usuallydescribes conditions orenvironments)Venus, with a surface temperature that would turnrubber to liquid, is inimical to any form of life.incorrigible(adjective): impervious tocorrection by punishment Tom Sawyer seems like an incorrigible youth until Huck Finn enters the novel; even Sawyer can't match his fierce individual spirit.inexorable(adjective): impossible to stop orprevent The rise of the computer was an inexorable shift in technology and culture.impudent(adjective): improperly forward orbold In an impudent move, the defendant spoke out of order to say terribly insulting things to the judge.copious(adjective): in abundant supply In midsummer, there are copious popiscle stands atthe beach; in the winter, there are none.subversive(adjective): in opposition to a civilauthority or government The ruling political party has begun a campaign to shut down subversive websites that it deems as a threat to "national safety."irrevocable(adjective): incapable of beingretracted or revoked Once you enter your plea to the court, it is irrevocable so think carefully about what you will say.implacable(adjective): incapable of making lessangry or hostile Win or lose, the coach was always implacable, never giving the athletes an easy practice or a break.soporific(adjective): inducing mentallethargy; sleep inducing Although the professor is brilliant, his bland monotone gives his lectures a soporific effect.didactic(adjective): instructive (especiallyexcessively) Tolstoy's The Death of Ivan Illyich is a didactic novel, instructing the reader on how to live a good life.prolific(adjective): intellectually productive Schubert was the most prolific composer, producinghundreds of hours of music before he died at the age of31.ostentatious (adjective): intended to attractnotice and impress others; tawdryor vulgarMatt wanted to buy stone lions for front of the house,but Cynthia convinced him that such a display wouldbe too ostentatious for a modest house in anunassuming neighborhood.obscure(adjective): known by only a few Many of the biggest movie stars were once obscure actors who got only bit roles in long forgotten films. This word has other definitions but this is the most important one for the GREwanting(adjective): lacking She did not think her vocabulary was wanting, yetthere were so many words that inevitably she found afew she didn't know.myopic(adjective): lacking foresight orimagination The company ultimately went out of business because the myopic managers couldn't predict the changes in their industry. This word has other definitions but this is the most important one for the GREpedestrian(adjective): lacking imagination While Nan was always engaged in philosophical speculation, her brother was occupied with far more pedestrian concerns: how to earn a salary and run a household. This word has other definitions but this is the most important one for the GREincongruous(adjective): lacking in harmony orcompatibility or appropriateness The vast economic inequality of modern society is incongruous with America's ideals.bumbling (adjective): lacking physicalmovement skills, especially with thehandsWithin a week of starting, the bumbling new waiterwas unceremoniously fired.hackneyed(adjective): lacking significancethrough having been overused Cheryl rolled her eyes when she heard the lecturer's hackneyed advice to "be true to yourself."gauche(adjective): lacking social polish Sylvester says the most gauche things, such as telling agirl he liked that she was much prettier when she woremakeup.ephemeral(adjective): lasting a very short time The lifespan of a mayfly is ephemeral, lasting from afew hours to a couple of days.transient(adjective): lasting a very short time The unpredictable and transient nature of deja vumakes it a very difficult phenomenon to study properly.apathetic(adjective): marked by a lack ofinterest Mr. Thompson was so talented at teaching math that even normally apathetic students took interest.pedantic (adjective): marked by a narrowfocus on or display of learningespecially its trivial aspectsProfessor Thompson was regarded as an expert in hisfield, but his lectures were utterly pedantic, focused onrigorous details of the most trivial conventions in thefield.meticulous(adjective): marked by extreme carein treatment of details The Japanese noodle maker was meticulous in making his noodles and would never let another person take over the task.vehement(adjective): marked by extremeintensity of emotions or convictions While the other employees responded to the bad news in a measured way, Andrew responded in a vehement manner, tipping over his desk and shouting at the top of his lungs.haphazard (adjective): marked by greatcarelessness; dependent upon orcharacterized by chanceMany golf courses are designed with great care, butthe greens on the county golf course seem entirelyhaphazard.forlorn(adjective): marked by or showinghopelessness After her third pet dog died, Marcia was simply forlorn: this time even the possibility of buying a new dog no longer held any joy.furtive (adjective): marked by quiet andcaution and secrecy; taking pains toavoid being observedWhile at work, George and his boss Regina felt theneed to be as furtive as possible about their romanticrelationship.tortuous (adjective): marked by repeatedturns and bends; notstraightforwardBecause the logic behind McMahon's side of thedebate was so tortuous, his audience came out eithercompletely confused or, worse, feeling they'd beentricked.aberrant(adjective): markedly different froman accepted norm When the financial director started screaming and throwing food at his co-workers, the police had to come in to deal with his aberrant behavior.ambivalent(adjective): mixed or conflictingemotions about something Sam was ambivalent about studying for the exam because doing so ate up a lot of his time, yet he was able to improve his analytical skills.tempered(adjective): moderated in effect The wide-eyed optimism of her youth was nowtempered after she had worked many years in thecriminal justice system.superfluous(adjective): more than is needed,desired, or required Everything in this closet is superfluous and can be given to charity.cryptic(adjective): mysterious or vague,usually intentionally Since Sarah did not want her husband to guess the Christmas present she had bought him, she only answered cryptically when he would ask her questions about it.parochial(adjective): narrowly restricted inscope or outlook Jasmine was sad to admit it, but her fledgling relationship with Jacob did not work out because his culinary tastes were simply too parochial; "After all," she quipped on her blog, "he considered Chef Boyardee ethnic food."magnanimous (adjective): noble and generous inspirit, especially towards a rival orsomeone lesspowerful He was a great sportsman: in defeat he wascomplementary and in victory he was magnanimous.immutable(adjective): not able to be changed Taxes are one of the immutable laws of the land, sothere is no use arguing about paying them.opaque(adjective): not clearly understoodor expressed The meaning of the professor's new research was opaque to most people, so no one asked any questions. This word has other definitions but this is the most important one for the GREinscrutable(adjective): not easily understood;unfathomable His speech was so dense and confusing that many in the audience found it inscrutable.indecorous (adjective): not in keeping withaccepted standards of what is rightor proper in politesociety Eating with elbows on the table is consideredindecorous in refined circles.languid (adjective): not inclined towardsphysical exertion or effort; slow andrelaxedAs the sun beat down and the temperature climbedhigher, we spent a languid week lying around thehouse.anomalous(adjective): not normal According to those who do not believe in climate change, the extreme weather over the last five years is simply anomalous--average temps should return to average, they believe.frivolous(adjective): not serious in content orattitude or behavior Compared to Juliet's passionate concern for human rights, Jake's non-stop concern about football seems somewhat frivolous.frugal(adjective): not spending muchmoney (but spending wisely) Monte was no miser, but was simply frugal, wisely spending the little that he earned.imprudent(adjective): not wise Hitler, like Napoleon, made the imprudent move ofinvading Russia in winter, suffering even morecasualties than Napoleon had.fortuitous (adjective): occurring by happychance; having no cause or apparentcauseWhile the real objects are vastly different sizes inspace, the sun and the moon seem to have the samefortuitous size in the sky.fallacious(adjective): of a belief that is basedon faulty reasoning The widespread belief that Eskimos have forty different words for snow is fallacious, based on one false report.laconic(adjective): one who says very fewwords While Martha always swooned over the hunky, laconic types in romantic comedies, her boyfriends inevitably were very talkative--and not very hunky.ambiguous(adjective): open to more than oneinterpretation The coach told his team, "Move towards that side of the field"; because he did not point, his directions were ambiguous, and the team had no idea to which side he was referring.fastidious(adjective): overly concerned withdetails; fussy Whitney is fastidious about her shoes, arranging them on a shelf in a specific order, each pair evenly spaced.mawkish(adjective): overly sentimental tothe point that it is disgusting The film was incredibly mawkish, introducing highly likeable characters only to have them succumb to a devastating illnesses by the end of the movie.craven(adjective): pathetically cowardly Though the man could have at least alerted the police,he crouched cravenly in the corner as the old womanwas mugged.specious(adjective): plausible but false He made a career out of specious arguments and fictional lab results, but lost his job and reputation when his lies were exposed by an article in The New York Times.spurious(adjective): plausible but false When listening to a politician speak, it is hard todistinguish the spurious claims from the authenticones.contingent(adjective): possible but not certainto occur Whether the former world champions can win again this year is contingent upon none of its star players getting injured.ascetic(adjective): practicing self-denial His ascetic life is the main reason he inspired so manyfollowers, especially since he gave up wealth and powerto live in poverty.austere(adjective): practicing self-denial His lifestyle of revelry and luxurious excess couldhardly be called austere.propitious (adjective): presenting favorablecircumstances; likely to result in orshow signs of successThe child's heartbeat is still weak, but I am seeingmany propitious signs and I think that she may behealing.efficacious(adjective): producing the intendedresult Since Maggie's cough syrup, which had expired five years back, was no longer efficacious, she coughed through the night.。
财务英语英汉对照表
财务英语英汉对照表return on stockholders’ equity股东产权收益率return on common stock equity一般股产权收益率return on sales销售收益率receivables turnover应收帐款周转率return on investment投资收益率return in equity产权收益率racial discrimination种族鄙视racketeering敲诈，诈骗radical school of accounting theory激进学派会计理论radical unionism激进工会主义raid掠夺股权，盗用，挪用raider firm掠夺性企业raised check涂改支票raising funds筹措资金rake-off受贿R&D company研究和进展专业公司R&D cost研究和进展成本random随机random access随机存取random access memory随机存取储备器random sampling随机抽样法random variance随机变量random walk theory 随机闲逛理论range全距，幅距rank登记，顺序ranking of projects投资项目排列顺序rapid amortization快速摊销ratable value应税价值rate比率rate anticipation swap利率预期掉换rate cutting费率削减rate fixing费率核定rate of discount贴现率，折现率rate of dividend股利率rate of interest利率rate of return on investment 投资收益率rate of return on sales销售收益率rate of return on equity产权收益率rate per annum年率rate per diem日率rate per mensem月率rate regulation费率管制rate risk汇率风险，利率风险rates地点税rates relief地点税减免rates support grant地点税补助拨款rate variance工资率差异ratification认可，批准rating评定信用等级rating agency信用等级评定机构ratio比率ratio analysis比率分析ratio analysis method比率分析法ratio chart比率图表ratio covenant比率保证条款ratio estimation比率推算法rationalized production合理化生产ratio of current asset to current liability流淌资产对流淌负债比率ratio of current asset to total asset流淌资产对资产总额比率ratio of current liability to total liability流淌负债对负债总额比率ratio of dependence on foreigntrade外贸依存率ratio of fixed asset to capital固定资产对资本比率ratio of fixed to total assets固定资产对总资产比率ratio of inventory to net sales存货对销售净额比率ratio of net income to net sales净收益对销售净额比率ratio of net income to equity净收益对资本净值比率ratio of quick asset to current liability速动资产对流淌负债比率ratio of receivable to net sales应收帐款对销售净额比率ratio of sales to cost销售成本率ratio of total liability to equity负债总额对资本净值比率raw data原始数据raw material inventory原材料存货r_base个人电子运算机数据库治理程序reacquired bond购回债券reacquired stock购回股票read阅读reader阅读器readjustable bond可调整利率债券readjusting entry帐务重新调整分录read-write memory读写储备器ready cash现金，现款ready sale适销，畅销ready shipment即期装运Reaganomics里根经济学real实物的，实际的，不动产的，房地产的real account实帐户real capital实物资本real cost实物成本，实际成本real estate房地产，不动产real estate agent不动产经纪人real estate income不动产收益real estate investment不动产投资real estate investment trust不动产投资信托公司real estate loan不动产贷款real estate market不动产市场real estate mortgage不动产抵押real estate mortgage bond不动产抵押债券real estate portfolio不动产组合投资real estate tax不动产税real gross national product实际国民生产总值real income实际收入，实际收益real investment实际投资realizability变现能力realizable asset可变现资产realizable value可变现价值realizable value accounting变现价值会计realization实现，变现realization and liquidation account变现清算帐户realization and liquidation statement资产清算表realization convention 实现常规realization principle实现原则realized gain or loss已实现损益realized value变现价值real national income实际国民收入real personal disposable income个人可支配的实际收入real property不动产real rate of interest实际利率real-time information system实时信息系统real-time processing实时处理realty不动产real value实际价值real wage实际工资rearrangement of debt重新安排债务reasonableness check合理性抽查，合理性校验reasonable value合理价值reassessment重估价rebate回扣，退税rebate card回扣信用卡rebudgeting重编预算recapitalization重组资本recapture clause收回权益条款recapture of earnings超额收益的归国有receipt收入，现金收入；收据receivables应收款项receivables financing应收款项融通资金receivables turnover应收帐款周转率receiver收款人，破产企业财产接管人receivership accounting破产清算责任会计receiving order接管指令receiving report收货报告单，收货单recession衰退reciprocal account相互往来帐户reciprocal allocation method相互分配法，相互分摊法reciprocal buying互购，互买reciprocal holdings相互控股reciprocal tariff互惠关税reciprocal trade互惠贸易reclassify再分类recognition criteria确认标准recognition of expense费用确认recognition of revenue营业收入确认recognition principle确认原则recognition rule确认规则reconciliation 调剂reconciliation statement调剂表reconciliation working sheet调整工作底稿recontract重订合同record记录record date列册日期recording medium记帐媒介records protection记录爱护records retrntion记录储存recoup补偿recourse追索权recoverable amount可收回金额recoverable cost可回收成本recovery复苏，回收recovery value回收价值recurring audit经常性审计recurring costs经常性成本red balance赤字余额red clause letter of credit红条款信用证redeemable bond可赎回债券redeemable preferred stock可赎回优先股redemption赎回，偿还redemption fund偿债基金redemption period赎回期，偿还期redemption premium赎回溢价redemption price赎回价格，兑回价格redemption yield兑回收益率，兑现收益率redevelopment再开发red flag红色信号red-herring prospectus红色招股说明书red risk赤字，亏损red-ink entry红字分录rediscount转贴现，再贴现rediscount rate转贴现率，再贴现率redistributed cost再分配成本redistribution of income收入再分配redistribution of wealth财宝再分配reducing-balance method 余额递减折旧法reduction of capital缩减资本，减资redundancy payment解雇津贴reexport再出口，转口referee公断人，后备付款人reference资信证明信，资信证明材料；索引，查帐索引reference book资信手册refinancing重筹资本reflation通货复帐reform改革reformation of economic system经济制度改革refugee capital逃亡资本refund退款，退税；兑换证券，调换证券refunding bond调换债券regional cpa firms地区性会计事务所regional economic integration地区经济一体化regional network地区网络regional stock exchange地区性股票交易所regional trading arrangements地区贸易安排register登记薄，寄存器registered auditor注册审计师registered bond记名债券registered bookkeeper注册薄记师registered business programmer注册企业程序师registered capital注册资本registered stock记名股票registered trademark注册商标register of directors and secretaries公司董事和秘书登记薄register of members股东登记薄register of transfer转让登记薄registrar注册治理机构，注册治理官员registrar in bankruptcy破产注册治理局registrar of company公司注册治理局registration登记，注册registration statement申请上市注册报表regression analysis回来分析regression coefficient回来系数regressive tax递减税，累退税regular audit常规审计regular dividend正常股利regular income固定收入，固定收益regular rate正常工资率，常规利率regular tax正税regulation条例，规章regulation of corporate financial reporting公司会计报表条例，公司会计报表规章regulation S-T规章，申请上市电子注册会计报表规章regulation S-X规章，申请上市注册会计报表内容和格式规章regulatory tax克制税rehabilitation cost修复成本rehypothecate再抵押reimbursable expenditure可补偿支出reimbursement偿付reimbursing bank偿付银行reinsurance分保，再保险reinvestment再投资reinvestment privilege再投资特权reinvestment rate再投资率reinvestment risk再投资风险related company联营公司related cost关联成本related fund关联基金related party transaction关联人士交易，内幕交易relative cost advantage相对成本优势relative fixed cost相对固定成本relative priority相对优先求偿权relative risk相关风险relative sales value method相对销售价值法relative volatility相对变动性release舍弃权益，解除抵押relevance相关性relevance principle相关性原则relevant cost相关成本relevant range相关范畴reliability 可靠性，可靠程度reliability principle可靠性原则reliance on internal control对内部操纵制度的信任程度relief救济，剔除，减免remittance汇付，汇款remittee收款人remitter汇款人remitting bank托收银行，汇款银行remortgage转抵押，再抵押remote terminal远程终端机removal cost拆迁成本remuneration酬劳renegotiation重议价renewal更新，展期rent租用，租金rental expense租赁费用rental income租赁收益rent-purchase租购reorder cost订货成本，再订货成本reorder point订货点，再订货点reorder quantity订货量reorganization公司改组，公司重组reorganization bond公司改组债券reorganization plan公司改组打算，公司重组打算repairs and maintenance修理费repatriation restriction汇出利润限制repayment偿还，偿付repeating audit重复性审计repeating decision重复性决策replacement cost重置成本replacement cost accounting重置成本会计replacement cost insurance重置成本保险replacement value重置价值repledge转押replevin归还产权repo再回购协议report 年度报告，审计报告report form报告式reporting currency报告货币reporting objectives报告目标reporting period报告期reporting policies报告政策reporting postulate报告假设reporting standard for audit审计报告准则repossession已售商品收回representation情形申诉，情形说明representation and warranties情形申诉和保证representative firm代表性企业representative sample代表性样本repressed inflation抑止性通货膨胀reproduction cost再生产成本reprivatization发还私营repudiation拒付债务repurchase agreement再购回协议repurchased stock购回股份request for proposal要求投标，招标required deposit balance规定存款余额required rate of return期望收益率requisition请购单，领料单resale转售resale price转售价格resale value转售价值rescheduling of debt债务重议rescission解约research and development研究和开发research and development cost研究和开发成本research intensive研究密集research libraries information network研究性图书信息网络reservation权益保留reserve预备，预备金,公积金reserve accounting 公积金会计reserve currency储备货币reserve for accidents意外事故预备金reserve for depreciation折旧预备reserve fund预备金，公积金residual asset剩余资产residual claim剩余索赔权residual cost剩余成本residual equity剩余股权residual equity theory剩余产权论residual income剩余收益额residual theory of dividend剩余股利理论residual value剩余价值resolution决议resource资源，资财resource allocation资源分配resource budget资源预算resource-oriented production面向资源生产resources conservation资源爱护resource sharing资源分享respondentia船货抵押借款responsibility accounting责任会计responsibility budget责任预算responsibility center责任中心responsibility costing责任成本运算法restatement of financial statement重编财务报表，重编会计报表restitution赔偿，偿还restraint of trade贸易约束restricted cash限定用途现金restricted fund限定用途基金restricted retained earning限定用途留存收益restricted security限制公布发行的证券restrictive covenant限制性条款restrictive endorsement限定背书restrictive policy限制性政策restructuring of debt债务重定，债务调整results from operation经营成果retail accounting零售会计retail audit零售审计retail cost零售成本retail method 零售盘存法retail price零售价retail price index零售价格指数retained earnings留存收益，留存盈余retained earnings policy 留存盈余政策，留存收益政策retained earnings statement 留存盈余表，留存收益表retained earnings to net worth ratio留存收益对资本净值比率retained income 留存收益retained profit 留存利润retention money 扣留款项，保留款项;留存资金retention ratio 留存比率retirement退役，报废；退股，还本；退休retirement benefit退休金retirement fund资产重置基金；退休金基金retirement of bond债券偿兑retirement of stock股票退股retirement plan退休打算，退休方法retirement policy退休政策retrenchement紧缩开支retrieval检索retroactive adjustment追溯调整retroactive pay追补工资return酬劳，收益；纳税申报表，税单returned check退回支票returned goods退回物资returned of capital资本退回，资本收回return on assets资产收益率return on capital资本收益，资本收益率，投资收益率return on common equity一般股产权资本收益率return on equity 产权资本收益率return on investment投资酬劳率，投资收益率return on sales销售收益率return on total assets资产总额收益率revalorization of currency币值重定revaluation重估价revaluation of assets资产重估价revaluation of currency币值重估revaluation reserve重估价预备金revaluation surplus重估价盈余revenue收入，营业收入；岁入，税收revenue account营业收入帐户，岁入帐户revenue and expense account收入和费用汇总帐户revenue anticipation note待付税款票据revenue bond收益担保债券revenue center收入中心revenue-cost graph收入成本图表revenue expenditure营业支出revenue-expense view收入－费用观念revenue recognition 收入确认，营业收入确认revenue recognition principle收入确认原则revenue reserve营业公积金reversal cost method倒轧成本法reverse dumping反向倾销reverse entry转回分录reverse income tax反向所得税reverse leverage反向杠杆作用reverse splitup并股reverse yield gap反向收益率差距review检查，复核revocable credit可撤销贷款revocable letter of credit可撤销信用证revocable trust可撤销信托revolving charge account循环赊帐帐户revolving credit循环信贷，循环贷款revolving credit agreement循环信贷协议revolving fund周转金revolving letter of credit循环信用证reward奖金，酬劳right权益，认股权，购股权right of absolute priority绝对优先求偿权right of action起诉权，诉讼权right of execution执行权right of first refusal第一拒绝权right of lien留置权right of offset抵消权right of recourse追索权right of redemption赎回权right of subrogation取代债权，取代追索权right of way地役权rights issue 附权发行rights letter购股权证书rights on附权，附认购新股权rights out除权rigid price僵硬价格ring操纵市场集团risk风险risk-adjusted discount factor 险调整折现系数risk-adjusted rate of return风险调整收益率risk analysis风险分析risk and return relationship风险和收益地关系risk averter风险厌恶者risk capital风险本risk consulting风险咨询risk diversification风险分散risk exposure风险暴露程度risk index风险指数riskless portfolio无风险证券组合投资riskless rate of return无风险投资收益率risk lover风险爱好投资人risk management风险治理risk manager风险经理risk premium风险酬劳，风险溢酬risk-return analysis风险收益分析risk-return frontier风险收益边界risk-return trade-off风险收益选择rock bottom price最低价rocks财务窘迫rolling budget滚动预算rollover转期rotation of auditor审计师轮换rotation of capital资本循环，资本周转rotation of directors公司董事轮换round lot整批数量，整批round off 去掉尾数，四舍五入round sum整数round transaction整套交易round-tripping迂回套利royalty租费，版税，开采权使用费，专利使用费，技术转让使用费royalty payment专利权转让使用费，技术转让提出费rubber check空头支票rule 规则，实施细则，运算法则rule off划线结传rule of seventy-eight 78规则，贷款利息运算公式rule of seventy-two72规则，投资本利和金额运算公式rules of thumb约略估量方法run挤兑runaway inflation急骤上涨的通货膨胀running ccount未结清帐户，赊帐帐户running cost运转成本running credit周转信贷running expense日常费用running form流水式running in ventory永续盘存running margin经营利差running yield本期收益率Rutgers accounting web新泽西州立大学会计互联网。
random模块详细用法大全
random模块详细⽤法⼤全 random.seed(a=None, version=2) 初始化随机数⽣成器。
如果 a 被省略或为 None ，则使⽤当前系统时间。
如果操作系统提供随机源，则使⽤它们⽽不是系统时间（有关可⽤性的详细信息，请参阅 os.urandom() 函数）。
如果 a 是 int 类型，则直接使⽤。
对于版本2（默认的），str 、 bytes 或 bytearray 对象转换为 int 并使⽤它的所有位。
对于版本1（⽤于从旧版本的Python再现随机序列），⽤于 str 和 bytes 的算法⽣成更窄的种⼦范围。
在 3.2 版更改: 已移⾄版本2⽅案，该⽅案使⽤字符串种⼦中的所有位。
random.getstate() 返回捕获⽣成器当前内部状态的对象。
这个对象可以传递给 setstate() 来恢复状态。
random.setstate(state) state 应该是从之前调⽤ getstate() 获得的，并且 setstate() 将⽣成器的内部状态恢复到 getstate() 被调⽤时的状态。
random.getrandbits(k) 返回带有 k 位随机的Python整数。
此⽅法随 MersenneTwister ⽣成器⼀起提供，其他⼀些⽣成器也可以将其作为API的可选部分提供。
如果可⽤，getrandbits() 启⽤ randrange() 来处理任意⼤范围。
整数⽤函数 random.randrange(stop) random.randrange(start, stop[, step]) 从 range(start, stop, step) 返回⼀个随机选择的元素。
这相当于 choice(range(start, stop, step)) ，但实际上并没有构建⼀个 range 对象。
位置参数模式匹配 range() 。
不应使⽤关键字参数，因为该函数可能以意外的⽅式使⽤它们。
random函数详解
#include <iostream>#include <time.h>using namespace std;#define MAX 100int main(int argc, char* argv[]){srand( (unsigned)time( NULL ) ); //srand()函数产生一个以当前时间开始的随机种子for (int i=0;i<10;i++)cout<<rand()%MAX<<endl; //MAX为最大值，其随机域为0~MAX-1 return 0;}rand()通常的使用方法是这样的：rand()不需要参数，它会返回一个从0到最大随机数的任意整数，最大随机数的大小通常是固定的一个大整数。
这样，如果你要产生0~10的10个整数，可以表达为：int N = rand() % 11;这样，N的值就是一个0~10的随机数，如果要产生1~10，则是这样：int N = 1 + rand() % 11;总结来说，可以表示为：a + rand() % n其中的a是起始值，n是整数的范围。
若要0~1的小数，则可以先取得0~10的整数，然后均除以10即可得到随机到十分位的10个随机小数，若要得到随机到百分位的随机小数，则需要先得到0~100的10个整数，然后均除以100，其它情况依此类推。
通常rand()产生的随机数在每次运行的时候都是与上一次相同的，这是有意这样设计的，是为了便于程序的调试。
若要产生每次不同的随机数，可以使用srand( seed )函数进行随机化，随着seed的不同，就能够产生不同的随机数。
如大家所说，还可以包含time.h头文件，然后使用srand( time(0))来使用当前时间使随机数发生器随机化，这样就可以保证每两次运行时可以得到不同的随机数序列(只要两次运行的间隔超过1秒)。
random函数详解开始是介绍一下random()函数和Math.random()函数,然后介绍一些由此引出的自定义函数.对于如何实战出一些效果,那需要想象的翅膀和其它AS基础的支持.而算法本身并不困难.最后我会介绍一个简单效果.希望能启发读者的思维.1、random(number)函数介绍见帮助文档,简单再提一下,random(number)返回一个0~number-1之间的随机整数.参数number代表一个整数.示例:trace(random(5));//复制到主场景第一帧.2、Math.random()见帮助文档。
random类的方法
random类的方法Random 类是 Java 中用来生成随机数的类，它提供了多种方法来生成不同类型的随机数。
下面是 Random 类的常用方法：1. nextBoolean()：返回一个随机的 boolean 值。
```javaRandom rand = new Random();boolean randomBoolean = rand.nextBoolean();```2. nextInt()：返回一个随机的 int 值。
```javaRandom rand = new Random();int randomNumber = rand.nextInt();```3. nextInt(int n)：返回一个小于 n 的非负随机整数。
```javaRandom rand = new Random();int randomNumber = rand.nextInt(10); // 返回一个小于 10 的非负整数```4. nextLong()：返回一个随机的 long 值。
```javaRandom rand = new Random();long randomNumber = rand.nextLong();```5. nextFloat()：返回一个随机的 float 值。
范围是 [0.0, 1.0)。
```javaRandom rand = new Random();float randomFloat = rand.nextFloat();```6. nextDouble()：返回一个随机的 double 值。
范围是 [0.0, 1.0)。
```javaRandom rand = new Random();double randomDouble = rand.nextDouble();```7. setSeed(long seed)：设置随机数生成器的种子，使用相同的种子将会生成相同的随机数序列。
random库的使用
random库的使⽤⼀、random库介绍random库是使⽤随机数的Python标准库伪随机数：采⽤梅森旋转算法⽣成的(伪)随机序列中元素random库主要⽤于⽣成随机数使⽤random库：import random1.1 random库概述random库包括两类函数，常⽤共8个基本随机数函数： seed(), random()扩展随机数函数：randint(), getrandbits(), uniform(),randrange(), choice(), shuffle()⼆、基本随机数函数2.1随机数种⼦[]函数描述seed(a=None)初始化给定的随机数种⼦，默认为当前系统时间random()⽣成⼀个[0.0, 1.0)之间的随机⼩数import randomrandom.seed(10) # 产⽣种⼦10对应的序列random.random()结果：0.5714025946899135random.random()结果：0.4288890546751146random.seed(10)random.random()结果：0.5714025946899135三、扩展随机数函数函数描述randint(a,b)⽣成⼀个[a, b]之间的整数randrange(m, n[, k])⽣成⼀个[m, n)之间以k为步长的随机整数getrandbits(k)getrandbits(k)uniform(a, b)⽣成⼀个[a, b]之间的随机⼩数choice(seq)从序列seq中随机选择⼀个元素shuffle(seq)将序列seq中元素随机排列，返回打乱后的序列eg: randint()import randomrandom.randint(10, 100)结果：60eg:randrange()import randomrandom.randrange(10, 100, 10)结果：80eg:getrandbits()import randomrandom.getrandbits(16)结果：37885eg:uniform()import randomrandom.uniform(10, 100)结果：11.334920142209832eg:choice()import randomrandom.choice([1, 2, 3, 4, 5, 6, 7])结果：5eg:shuffle()import randoms = [1, 2, 3, 4, 5, 6, 7, 8, 9]random.shuffle(s)print(s)结果：[3, 9, 7, 4, 1, 2, 6, 5, 8]3.1 随机函数的使⽤需要掌握的能⼒能够利⽤随机数种⼦产⽣"确定"伪随机数能够产⽣随机整数能够对序列类型进⾏随机操作四、圆周率的计算蒙特卡洛⽅法from random import randomfrom time import perf_counterDARTS = 1000 * 1000hits = 0.0start = perf_counter()afor i in range(1, DARTS + 1):x, y = random(), random()dist = pow(x**2 + y**2, 0.5)if dist <= 1.0:hits = hits + 1pi = 4 * (hits / DARTS)print("圆周率值是: {}".format(pi))print("运⾏时间是: {:.5f}s".format(perf_counter() - start))。
SAS_9——精选推荐
TUTORIAL 9: Random and Mixed effects ANOVAI. Random and Mixed effects ANOVATo date we have been concerned with constructing ANOVA models in which the factors have a predetermined set of levels. This type of model is often referred to as a fixed effects model. These models are appropriate for studies where our interest centers on the effects of the specific factor levels chosen, and they are the only levels that are considered relevant.Often the factor levels can be seen as a sample from a population of potential factor levels and inference is designed about the population of levels. In this situation the factor is considered to be a random variable and using a fixed-effects model is no longer appropriate. In the two-way ANOVA case, there are a variety of possible scenarios that we can potentially study. When both factors are random, we use a random effects model. When one factor is random and the other is fixed we use a mixed-effects model.PROC GLM and PROC MIXED are two procedures in SAS designed for analyzing random and mixed effects models. For more complicated models PROC MIXED is the most appropriate choice. However, for the models we will be analyzing in this class PROC GLM will suffice.To fit random and mixed effects models in PROC GLM we need to introduce a new statement. The RANDOM statement in PROC GLM declares that one or more effects in the model should be considered random rather than fixed. The general form of PROC GLM for fitting random and mixed-effects models is,PROC GLM data = data set;CLASS variables; /* Identifies the variables that divide the data setinto groups.MODEL response variable = explanatory variables;RANDOM random variables; /* Identifies the random effectsRUN;All the other statements are used in a similar manner as they were in the one-way and two-way ANOVA case. The only difference is the inclusion of the RANDOM statement.Suppose A and B are factors in a two-way ANOVA model and y specifies the response variable. As before, the MODEL statement is used to define the format of the model. To define a model without an interaction term we write:MODEL y = A B;To instead define a model with an interaction term we write:MODEL y = A | B;The RANDOM statement is used to define which parts of the model are considered random.Consider the model with an interaction term included. The statement:RANDOM A | B;specifies that A, B and A*B are all random. This tells SAS to use a two-way random effects model. The statement:RANDOM A A*B;specifies that A and A*B are random, while B is fixed. This tells SAS to use a mixed-effects model.Once you include the RANDOM statement in your code, SAS will automatically calculate the expected mean squares and use this as a guide for choosing the appropriate tests. Including the option TEST after the RANDOM statement performs hypothesis tests for each effect specified in the model, using appropriate error terms as determined by the expected mean squares.Ex. A process engineer thinks the material used for the motor casing and the supply source of the bearings used in the motor both have an impact on the amount of motor vibration (in microns). He performs an experiment in which casings made of steel, aluminum and plastic were constructed using bearings from 5 randomly selected sources.Source1 2 3 4 5Steel 13.1 13.2 16.3 15.8 13.7 14.3 15.7 15.8 13.5 12.5Aluminum 15.0 14.8 15.7 16.4 13.9 14.3 13.7 14.2 13.4 13.8Plastic 14.0 14.3 17.2 16.7 12.4 12.3 14.4 13.9 13.2 13.1In this problem the material used for the casing can be considered fixed. The source of the bearings is a random effect as we are interested in studying all possible sources. We will therefore assume that the source and interaction terms are both random and use a mixed effects model.The code for performing a mixed effects analysis can be written as follows:DATA vibration;INPUT case $ source vib @@;DATALINES;S 1 13.1 S 1 13.2 S 2 16.3 S 2 15.8 S 3 13.7S 3 14.3 S 4 15.7 S 4 15.8 S 5 13.5 S 5 12.5A 1 15.0 A 1 14.8 A 2 15.7 A 2 16.4 A 3 13.9A 3 14.3 A 4 13.7 A 4 14.2 A 5 13.4 A 5 13.8P 1 14.0 P 1 14.3 P 2 17.2 P 2 16.7 P 3 12.4P 3 12.3 P 4 14.4 P 4 13.9 P 5 13.2 P 5 13.1;RUN;PROC GLM;CLASS case source;MODEL vib = case | source;RANDOM source source*case / TEST;RUN;This program gives rise to the following output:The GLM ProcedureDependent Variable: vibSum ofSource DF Squares Mean Square F Value Pr > F Model 14 48.98466667 3.49890476 31.43 <.0001Error 15 1.67000000 0.11133333Corrected Total 29 50.65466667R-Square Coeff Var Root MSE vib Mean0.967032 2.324662 0.333667 14.35333Source DF Type I SS Mean Square F Value Pr > Fcase 2 0.70466667 0.35233333 3.16 0.0713source 4 36.67466667 9.16866667 82.35 <.0001case*source 8 11.60533333 1.45066667 13.03 <.0001Source DF Type III SS Mean Square F Value Pr > Fcase 2 0.70466667 0.35233333 3.16 0.0713source 4 36.67466667 9.16866667 82.35 <.0001case*source 8 11.60533333 1.45066667 13.03 <.0001Source Type III Expected Mean Squarecase Var(Error) + 2 Var(case*source) + Q(case)source Var(Error) + 2 Var(case*source) + 6 Var(source) case*source Var(Error) + 2 Var(case*source)Tests of Hypotheses for Mixed Model Analysis of VarianceSource DF Type III SS Mean Square F Value Pr > Fcase 2 0.704667 0.352333 0.24 0.7899source 4 36.674667 9.168667 6.32 0.0135Error 8 11.605333 1.450667Error: MS(case*source)Source DF Type III SS Mean Square F Value Pr > Fcase*source 8 11.605333 1.450667 13.03 <.0001 Error: MS(Error) 15 1.670000 0.111333The relevant tests can be found below the table with the expected mean squares. Studying the output, the interaction between the material and the source of bearings is a significant source of variation (F = 13.03, p-value < 0.0001). The different casings by themselves do not appear to affect the amount of vibration (F = 0.24, p-value = 0.7899), though the interpretation of this test is clouded by the significant interaction. In addition, the main effect corresponding to the source is significant (F = 6.32, p-value < 0.0135).II. Repeated Measures ANOVARepeated measures designs are common in many settings (e.g. behavioral and life sciences). This type of design utilizes the same subject for each of the treatments under study. A repeated measures study may either involve several treatments or only a single treatment that is evaluated at different time points. When several measurements are taken on the same subject, the measurements tend to be correlated and this correlation needs to be accounted for in the model. Repeated measures ANOVA can be viewed as a generalization of the paired t-test. The model assumes that every pair of measurements has the same correlation coefficient across subjects and that the variance and covariances are homogenous across time (or treatment). This specific structure for the covariance is referred to as compound symmetry. Compound symmetry is usually not a realistic assumption when dealing with measurements over time, as measurements closer together are typically more highly correlated than measurements that are far apart. There exist adjustments (e.g. Greenhouse-Geisser and Huynh-Feldt) that can be used to correct the observed significance levels for unequal correlation coefficients.Prior to performing repeated measures ANOVA in SAS it is important that the data is organized in the appropriate format. Each row should include the repeated measurements from one subject. The first column should contain the subject identifier, and the remaining columns should contain the repeated measurements of the response variable (e.g. y1, y2,….yn if there is a total of n measurements on subject i). For example the following data contains four repeated measures on 3 subjects:120 24 28 28215 18 23 24318 19 24 23We can read this data into a SAS data set using the following code:DATA mydata;INPUT subject y1-y4;DATALINES;1 20 24 28 282 15 18 23 243 18 19 24 23;RUN;Note that in the INPUT statement we can refer to the four repeated measures as y1-y4, rather than listing all four variable names separately. This is especially convenient as the number of measures increases.In order to use PROC GLM to fit a repeated measures model, we need to include a new statement and make some edits to the MODEL statement. The REPEATED statement asks SAS to provide a number of appropriate tests in the output for testing hypothesis concerning repeated measures data.An example of a one-way repeated measure model for the data set described in the example above can be written as follows:PROC GLMMODEL y1-y4= \NOUNI;REPEATED factor_name;RUN:This code differs from a standard one-way ANOVA in a few important ways. As there is no specific group identification for the subjects, there is no need for a CLASS statement.In the MODEL statement all of the repeated measures of the response variable are written on the left-hand side of the model equation. In addition, there are no explanatory variables on the right-hand side of the model statement. The option NOUNI tells SAS not to run separate ANOVA models for each of the 4 repeated measures. This minimizes the amount of unnecessary output. Finally, the REPEATED statement tells SAS to provide the appropriate tests and to refer to the repeated factor as factor_name. Note that the name that you ultimately choose is arbitrary, and is meant to help guide you in reading the output. The name should not be the same as any variable name that already exists in the data set being analyzed and should conform to the usual conventions of SAS variable names.The REPEATED statement has a variety of options. The PRINTE option produces output regarding the partial correlation coefficients, as well as a test of the hypothesis that the covariance structure of the repeated measurements is such that the p-values from the F-test are valid. In particular, you can check that the compound symmetry assumption is valid by studying the partial correlation coefficients (the correlation between different measurements should be approximately equal) and the results of the test of sphericity.Ex. In a wine-judging competition, four different wines of the same vintage were judged by six experienced judges. The order of the wine presentation was randomized for each judge and the wines were tasted blindly. Each wine was scored on a 40-point scale – the higher the score, the better the wine.Judge Wine1 2 3 4120 24 28 28215 18 23 24318 19 24 23426 26 30 30522 24 28 26619 21 27 25Is there a significant difference in the mean score between the wines?The following code can be used to answer this question:DATA winedata;INPUT judge score1-score4;DATALINES;1 20 24 28 282 15 18 23 243 18 19 24 234 26 26 30 305 22 24 28 266 19 21 27 25;RUN;PROC GLM data = winedata;MODEL score1-score4 = /NOUNI;REPEATED wine /PRINTE;RUN;This code gives rise to the following output:The GLM ProcedureRepeated Measures Analysis of VariancePartial Correlation Coefficients from the Error SSCP Matrix / Prob > |r| DF = 5 score1 score2 score3 score4score1 1.000000 0.929670 0.924946 0.8404180.0072 0.0082 0.0362score2 0.929670 1.000000 0.975453 0.9216350.0072 0.0009 0.0090score3 0.924946 0.975453 1.000000 0.8943960.0082 0.0009 0.0161score4 0.840418 0.921635 0.894396 1.0000000.0362 0.0090 0.0161E = Error SSCP Matrixwine_N represents the contrast between the nth level of wine and the last wine_1 wine_2 wine_3wine_1 22.0000 10.0000 8.0000wine_2 10.0000 8.0000 6.0000wine_3 8.0000 6.0000 7.3333Partial Correlation Coefficients from the Error SSCP Matrix of theVariables Defined by the Specified Transformation / Prob > |r|DF = 5 wine_1 wine_2 wine_3wine_1 1.000000 0.753778 0.6298370.0835 0.1802wine_2 0.753778 1.000000 0.7833490.0835 0.0653wine_3 0.629837 0.783349 1.0000000.1802 0.0653Sphericity TestsMauchly'sVariables DF Criterion Chi-Square Pr > ChiSqTransformed Variates 5 0.1106961 8.1924883 0.1459Orthogonal Components 5 0.3515625 3.8910912 0.5652MANOVA Test Criteria and Exact F Statistics for the Hypothesis of no wine EffectH = Type III SSCP Matrix for wineE = Error SSCP MatrixS=1 M=0.5 N=0.5Statistic Value F Value Num DF Den DF Pr > FWilks' Lambda 0.02314815 42.20 3 3 0.0059Pillai's Trace 0.97685185 42.20 3 3 0.0059Hotelling-Lawley Trace 42.20000000 42.20 3 3 0.0059Roy's Greatest Root 42.20000000 42.20 3 3 0.0059Repeated Measures Analysis of VarianceUnivariate Tests of Hypotheses for Within Subject EffectsAdj Pr > FSource DF Type III SS Mean Square F Value Pr > F G - G H - Fwine 3 184.0000000 61.3333333 57.50 <.0001 <.0001 <.0001Error(wine) 15 16.0000000 1.0666667Greenhouse-Geisser Epsilon 0.6038Huynh-Feldt Epsilon 0.9270Studying the partial correlation coefficients does not show any great departures from compound symmetry. The sphericity tests confirm these results (p-value = 0.5652). To test for treatment effects we find that F = 57.50 (p-value < 0.0001). Hence, we can reject the null hypothesis of no difference in treatment means. The mean scores for the four wines differ.。
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RANDOM StatementRANDOM random-effects < / options > ;The RANDOM statement defines the random effects constituting the vector in the mixed model. It can be used to specify traditional variance component models (as in the VARCOMP procedure) and to specify random coefficients. The random effects can be classification or continuous, and multiple RANDOM statements are possible.Using notation from the "Mixed Models Theory"section, the purpose of the RANDOM statement is to define the Z matrix of the mixed model, the randomeffects in the vector, and the structure of G. The Z matrix is constructed exactly as the X matrix for the fixed effects, and the G matrix is constructed to correspond with the effects constituting Z. The structure of G is defined by using the TYPE= option.You can specify INTERCEPT (or INT) as a random effect to indicate the intercept. PROC MIXED does not include the intercept in the RANDOM statement by default as it does in the MODEL statement.You can specify the following options in the RANDOM statement after a slash (/).ALPHA=numberrequests that a t-type confidence interval be constructed for each of the random effect estimates with confidence level 1-number. The value of number must be between 0 and 1; the default is 0.05.CLrequests that t-type confidence limits be constructed for each of the random effect estimates. The confidence level is 0.95 by default;this can be changed with the ALPHA= option.Grequests that the estimated G matrix be displayed. PROC MIXEDdisplays blanks for values that are 0. If you specify the SUBJECT= option, then the block of the G matrix corresponding to the first subject is displayed. For ODS purposes, the name of the table is "G."GCdisplays the lower-triangular Cholesky root of the estimated Gmatrix according to the rules listed under the G option. For ODS purposes, the name of the table is "CholG."GCIdisplays the inverse Cholesky root of the estimated G matrixaccording to the rules listed under the G option. For ODS purposes, the name of the table is "InvCholG."GCORRdisplays the correlation matrix corresponding to the estimated Gmatrix according to the rules listed under the G option. For ODS purposes, the name of the table is "GCorr."GDATA=SAS-data-setrequests that the G matrix be read in from a SAS data set. This Gmatrix is assumed to be known; therefore, only R-side parameters from effects in the REPEATED statement are included in theNewton-Raphson iterations. If no REPEATED statement is specified, then only a residual variance is estimated.The information in the GDATA= data set can appear in one of two ways.The first is a sparse representation for which you include ROW, COL, and VALUE variables to indicate the row, column, and value of G.All unspecified locations are assumed to be 0. The secondrepresentation is for dense matrices. In it you include ROW and COL1 -COL n variables to indicate the row and columns of G, which is a symmetric matrix of order n. For both representations, you mustspecify effects in the RANDOM statement that generate a Z matrix that contains n columns. See Example 41.4.If you have more than one RANDOM statement, only one GDATA= option is required on any one of them, and the data set you specify must contain the entire G matrix defined by all of the RANDOM statements.If the GDATA= data set contains variance ratios instead of thevariances themselves, then use the RATIOS option.Known parameters of G can also be input using the PARMS statement with the HOLD= option.GIdisplays the inverse of the estimated G matrix according to therules listed under the G option. For ODS purposes, the name of the table is "InvG."GROUP=effectGRP=effectdefines an effect specifying heterogeneity in the covariancestructure of G. All observations having the same level of the group effect have the same covariance parameters. Each new level of the group effect produces a new set of covariance parameters with the same structure as the original group. You should exercise caution in defining the group effect, as strange covariance patterns can result with its misuse. Also, the group effect can greatly increase the number of estimated covariance parameters, which may adversely affect the optimization process.Continuous variables are permitted as arguments to the GROUP=option. PROC MIXED does not sort by the values of the continuous variable; rather, it considers the data to be from a new subject or group whenever the value of the continuous variable changes from the previous observation. Using a continuous variable decreasesexecution time for models with a large number of subjects or groups and also prevents the production of a large "Class LevelsInformation" table.LDATA=SAS-data-setreads the coefficient matrices associated with the TYPE=LIN(number) option. The data set must contain the variables PARM, ROW, COL1-COLn, or PARM, ROW, COL, VALUE. The PARM variable denotes which of the number coefficient matrices is currently being constructed, and the ROW, COL1 -COLn, or ROW, COL, VALUE variables specify the matrix values, as they do with the GDATA= option. Unspecified values of these matrices are set equal to 0.NOFULLZeliminates the columns in Z corresponding to missing levels ofrandom effects involving CLASS variables. By default, these columns are included in Z.RATIOSindicates that ratios with the residual variance are specified in the GDATA= data set instead of the covariance parameters themselves.The default GDATA= data set contains the individual covarianceparameters.SOLUTIONSrequests that the solution for the random-effects parameters be produced. Using notation from the "Mixed Models Theory" section, these estimates are the empirical best linear unbiased predictors(EBLUPs) . They can be useful for comparingthe random effects from different experimental units and can also be treated as residuals in performing diagnostics for your mixed model.The numbers displayed in the SE Pred column of the "Solution forRandom Effects" table are not the standard errors of thedisplayed in the Estimate column; rather, they are the standarderrors of predictions , where is the i th EBLUP andis the i th random-effect parameter.SUBJECT=effectSUB=effectidentifies the subjects in your mixed model. Complete independence is assumed across subjects; thus, for the RANDOM statement, the SUBJECT= option produces a block-diagonal structure in G withidentical blocks. The Z matrix is modified to accommodate thisblock-diagonality. In fact, specifying a subject effect isequivalent to nesting all other effects in the RANDOM statement within the subject effect.Continuous variables are permitted as arguments to the SUBJECT= option. PROC MIXED does not sort by the values of the continuous variable; rather, it considers the data to be from a new subject or group whenever the value of the continuous variable changes from the previous observation. Using a continuous variable decreasesexecution time for models with a large number of subjects or groups and also prevents the production of a large "Class LevelsInformation" table.When you specify the SUBJECT= option and a classification random effect, computations are usually much quicker if the levels of the random effect are duplicated within each level of the SUBJECT=effect.TYPE=covariance-structurespecifies the covariance structure of G. Valid values forcovariance-structure and their descriptions are listed in Table41.3and Table 41.4. Although a variety of structures are available,most applications call for either TYPE=VC or TYPE=UN. The TYPE=VC (variance components) option is the default structure, and itmodels a different variance component for each random effect.The TYPE=UN (unstructured) option is useful for correlated random coefficient models. For example,random intercept age / type=un subject=person;specifies a random intercept-slope model that has differentvariances for the intercept and slope and a covariance between them.You can also use TYPE=FA0(2) here to request a G estimate that is constrained to be nonnegative definite.If you are constructing your own columns of Z with continuousvariables, you can use the TYPE=TOEP(1) structure to group them together to have a common variance component. If you desire to have different covariance structures in different parts of G, you must use multiple RANDOM statements with different TYPE= options.V<=value-list>requests that blocks of the estimated V matrix be displayed. The first block determined by the SUBJECT= effect is the defaultdisplayed block. PROC MIXED displays entries that are 0 as blanks in the table.You can optionally use the value-list specification, whichindicates the subjects for which blocks of V are to be displayed.For example, the statementrandom int time / type=un subject=person v=1,3,7;displays block matrices for the first, third, and seventh persons.The table name for ODS purposes is "V".VC<=value-list>displays the Cholesky root of the blocks of the estimated V matrix.The value-list specification is the same as in the V= option. The table name for ODS purposes is "CholV".VCI<=value-list>displays the inverse of the Cholesky root of the blocks of theestimated V matrix. The value-list specification is the same as in the V= option. The table name for ODS purposes is "InvCholV".VCORR<=value-list>displays the correlation matrix corresponding to the blocks of the estimated V matrix. The value-list specification is the same as in the V= option. The table name for ODS purposes is "VCorr".VI<=value-list>displays the inverse of the blocks of the estimated V matrix. The value-list specification is the same as in the V= option. The table name for ODS purposes is "InvV".。