distribution function
数学专业词汇及翻译
数学专业词汇及翻译一、字母顺序表 (1)二、常用的数学英语表述 (7)三、代数英语（高端） (13)一、字母顺序表1、数学专业词汇Aabsolute value 绝对值 accept 接受 acceptable region 接受域additivity 可加性 adjusted 调整的 alternative hypothesis 对立假设analysis 分析analysis of covariance 协方差分析analysis of variance 方差分析 arithmetic mean 算术平均值 association 相关性assumption 假设 assumption checking 假设检验availability 有效度average 均值Bbalanced 平衡的 band 带宽 bar chart 条形图beta-distribution 贝塔分布 between groups 组间的 bias 偏倚 binomial distribution 二项分布 binomial test 二项检验Ccalculate 计算 case 个案 category 类别 center of gravity 重心central tendency 中心趋势chi-square distribution 卡方分布chi-square test 卡方检验classify 分类cluster analysis 聚类分析coefficient 系数 coefficient of correlation 相关系数collinearity 共线性 column 列 compare 比较 comparison 对照 components 构成，分量compound 复合的 confidence interval 置信区间 consistency 一致性 constant 常数continuous variable 连续变量 control charts 控制图 correlation 相关 covariance 协方差 covariance matrix 协方差矩阵critical point 临界点critical value 临界值crosstab 列联表cubic 三次的，立方的cubic term 三次项cumulative distribution function 累加分布函数 curve estimation 曲线估计Ddata 数据default 默认的definition 定义deleted residual 剔除残差density function 密度函数dependent variable 因变量description 描述design of experiment 试验设计deviations 差异df.(degree of freedom) 自由度diagnostic 诊断dimension 维discrete variable 离散变量discriminant function 判别函数discriminatory analysis 判别分析distance 距离distribution 分布D-optimal design D-优化设计Eeaqual 相等 effects of interaction 交互效应 efficiency 有效性eigenvalue 特征值equal size 等含量equation 方程error 误差estimate 估计estimation of parameters 参数估计estimations 估计量evaluate 衡量exact value 精确值expectation 期望expected value 期望值exponential 指数的exponential distributon 指数分布extreme value 极值F factor 因素，因子 factor analysis 因子分析 factor score 因子得分 factorial designs 析因设计factorial experiment 析因试验fit 拟合fitted line 拟合线fitted value 拟合值 fixed model 固定模型 fixed variable 固定变量fractional factorial design 部分析因设计frequency 频数F-test F检验full factorial design 完全析因设计function 函数Ggamma distribution 伽玛分布geometric mean 几何均值group 组Hharmomic mean 调和均值 heterogeneity 不齐性histogram 直方图homogeneity 齐性homogeneity of variance 方差齐性hypothesis 假设 hypothesis test 假设检验Iindependence 独立independent variable 自变量independent-samples 独立样本 index 指数 index of correlation 相关指数 interaction 交互作用 interclass correlation 组内相关 interval estimate 区间估计intraclass correlation 组间相关inverse 倒数的iterate 迭代Kkernal 核 Kolmogorov-Smirnov test柯尔莫哥洛夫-斯米诺夫检验 kurtosis 峰度Llarge sample problem 大样本问题layer 层least-significant difference 最小显著差数least-square estimation 最小二乘估计least-square method 最小二乘法 level 水平 level of significance 显著性水平leverage value 中心化杠杆值life 寿命life test 寿命试验likelihood function 似然函数 likelihood ratio test 似然比检验linear 线性的linear estimator 线性估计linear model 线性模型linear regression 线性回归linear relation 线性关系linear term 线性项logarithmic 对数的logarithms 对数 logistic 逻辑的 lost function 损失函数Mmain effect 主效应matrix 矩阵maximum 最大值maximum likelihood estimation 极大似然估计 mean squared deviation(MSD) 均方差 mean sum of square 均方和 measure 衡量 media 中位数 M-estimator M估计minimum 最小值missing values 缺失值mixed model 混合模型 mode 众数model 模型Monte Carle method 蒙特卡罗法moving average 移动平均值multicollinearity 多元共线性multiple comparison 多重比较multiple correlation 多重相关multiple correlation coefficient 复相关系数multiple correlation coefficient 多元相关系数multiple regression analysis 多元回归分析multiple regression equation 多元回归方程 multiple response 多响应 multivariate analysis 多元分析Nnegative relationship 负相关nonadditively 不可加性nonlinear 非线性nonlinear regression 非线性回归noparametric tests 非参数检验 normal distribution 正态分布null hypothesis 零假设 number of cases 个案数Oone-sample 单样本 one-tailed test 单侧检验 one-way ANOVA 单向方差分析one-way classification 单向分类optimal 优化的optimum allocation 最优配制 order 排序order statistics 次序统计量 origin 原点orthogonal 正交的 outliers 异常值Ppaired observations 成对观测数据paired-sample 成对样本parameter 参数parameter estimation 参数估计 partial correlation 偏相关partial correlation coefficient 偏相关系数 partial regression coefficient 偏回归系数percent 百分数percentiles 百分位数pie chart 饼图point estimate 点估计poisson distribution 泊松分布polynomial curve 多项式曲线polynomial regression 多项式回归polynomials 多项式positive relationship 正相关 power 幂P-P plot P-P概率图predict 预测predicted value 预测值prediction intervals 预测区间principal component analysis 主成分分析 proability 概率probability density function 概率密度函数 probit analysis 概率分析proportion 比例Qqadratic 二次的 Q-Q plot Q-Q概率图 quadratic term 二次项quality control 质量控制 quantitative 数量的，度量的 quartiles 四分位数Rrandom 随机的 random number 随机数 random number 随机数random sampling 随机取样random seed 随机数种子random variable 随机变量 randomization 随机化 range 极差rank 秩 rank correlation 秩相关 rank statistic 秩统计量 regression analysis 回归分析regression coefficient 回归系数regression line 回归线reject 拒绝rejection region 拒绝域relationship 关系reliability 可*性repeated 重复的report 报告，报表 residual 残差 residual sum of squares 剩余平方和response 响应risk function 风险函数robustness 稳健性 root mean square 标准差 row 行 run 游程run test 游程检验Sample 样本sample size 样本容量sample space 样本空间sampling 取样 sampling inspection 抽样检验 scatter chart 散点图S-curve S形曲线separately 单独地sets 集合sign test 符号检验significance 显著性significance level 显著性水平significance testing 显著性检验 significant 显著的，有效的 significant digits 有效数字 skewed distribution 偏态分布 skewness 偏度 small sample problem 小样本问题 smooth 平滑 sort 排序 soruces of variation 方差来源 space 空间 spread 扩展square 平方 standard deviation 标准离差 standard error of mean 均值的标准误差standardization 标准化 standardize 标准化 statistic 统计量 statistical quality control 统计质量控制 std. residual 标准残差 stepwise regression analysis 逐步回归stimulus 刺激strong assumption 强假设stud. deleted residual 学生化剔除残差stud. residual 学生化残差 subsamples 次级样本 sufficient statistic 充分统计量sum 和 sum of squares 平方和 summary 概括，综述Ttable 表t-distribution t分布test 检验test criterion 检验判据test for linearity 线性检验 test of goodness of fit 拟合优度检验 test of homogeneity 齐性检验test of independence 独立性检验test rules 检验法则 test statistics 检验统计量 testing function 检验函数time series 时间序列tolerance limits 容许限total 总共，和transformation 转换 treatment 处理 trimmed mean 截尾均值 true value 真值 t-test t检验 two-tailed test 双侧检验unbalanced 不平衡的unbiased estimation 无偏估计unbiasedness 无偏性 uniform distribution 均匀分布Vvalue of estimator 估计值 variable 变量 variance 方差 variance components 方差分量 variance ratio 方差比 various 不同的 vector 向量Wweight 加权，权重weighted average 加权平均值within groups 组内的ZZ score Z分数2. 最优化方法词汇英汉对照表Aactive constraint 活动约束 active set method 活动集法 analytic gradient 解析梯度approximate 近似 arbitrary 强制性的 argument 变量 attainment factor 达到因子Bbandwidth 带宽be equivalent to 等价于best-fit 最佳拟合bound 边界Ccoefficient 系数complex-value 复数值component 分量constant 常数constrained 有约束的constraint 约束constraint function 约束函数continuous 连续的converge 收敛cubic polynomial interpolation method三次多项式插值法 curve-fitting 曲线拟合Ddata-fitting 数据拟合default 默认的，默认的define 定义diagonal 对角的direct search method 直接搜索法direction of search 搜索方向 discontinuous 不连续eigenvalue 特征值empty matrix 空矩阵equality 等式exceeded 溢出的Ffeasible 可行的 feasible solution 可行解 finite-difference 有限差分 first-order 一阶GGauss-Newton method 高斯-牛顿法 goal attainment problem 目标达到问题 gradient 梯度 gradient method 梯度法Hhandle 句柄 Hessian matrix 海色矩阵Independent variables 独立变量inequality 不等式infeasibility 不可行性infeasible 不可行的initial feasible solution 初始可行解initialize 初始化inverse 逆 invoke 激活 iteration 迭代 iteration 迭代JJacobian 雅可比矩阵LLagrange multiplier 拉格朗日乘子large-scale 大型的least square 最小二乘 least squares sense 最小二乘意义上的 Levenberg-Marquardt method 列文伯格-马夸尔特法line search 一维搜索linear 线性的linear equality constraints 线性等式约束linear programming problem 线性规划问题 local solution 局部解M medium-scale 中型的minimize 最小化mixed quadratic and cubic polynomialinterpolation and extrapolation method 混合二次、三次多项式内插、外插法multiobjective 多目标的Nnonlinear 非线性的 norm 范数Oobjective function 目标函数observed data 测量数据optimization routine 优化过程optimize 优化optimizer 求解器over-determined system 超定系统Pparameter 参数partial derivatives 偏导数polynomial interpolation method 多项式插值法Qquadratic 二次的 quadratic interpolation method 二次内插法quadratic programming 二次规划Rreal-value 实数值 residuals 残差 robust 稳健的 robustness 稳健性，鲁棒性S scalar 标量semi-infinitely problem 半无限问题Sequential Quadratic Programming method 序列二次规划法 simplex search method 单纯形法solution 解sparse matrix 稀疏矩阵sparsity pattern 稀疏模式 sparsity structure 稀疏结构 starting point 初始点step length 步长subspace trust region method 子空间置信域法sum-of-squares 平方和 symmetric matrix 对称矩阵Ttermination message 终止信息 termination tolerance 终止容限 the exit condition 退出条件 the method of steepest descent 最速下降法 transpose 转置Uunconstrained 无约束的 under-determined system 负定系统Vvariable 变量 vector 矢量Wweighting matrix 加权矩阵3 样条词汇英汉对照表Aapproximation 逼近 array 数组 a spline in b-form/b-spline b 样条 a spline of polynomial piece /ppform spline 分段多项式样条Bbivariate spline function 二元样条函数 break/breaks 断点Ccoefficient/coefficients 系数cubic interpolation 三次插值/三次内插cubic polynomial 三次多项式 cubic smoothing spline 三次平滑样条 cubic spline 三次样条cubic spline interpolation 三次样条插值/三次样条内插 curve 曲线Ddegree of freedom 自由度 dimension 维数Eend conditions 约束条件input argument 输入参数interpolation 插值/内插 interval取值区间Kknot/knots 节点Lleast-squares approximation 最小二乘拟合Mmultiplicity 重次 multivariate function 多元函数Ooptional argument 可选参数 order 阶次 output argument 输出参数P point/points 数据点Rrational spline 有理样条 rounding error 舍入误差（相对误差）Sscalar 标量sequence 数列（数组）spline 样条spline approximation 样条逼近/样条拟合spline function 样条函数 spline curve 样条曲线spline interpolation 样条插值/样条内插spline surface 样条曲面 smoothing spline 平滑样条Ttolerance 允许精度Uunivariate function 一元函数Vvector 向量Wweight/weights 权重4 偏微分方程数值解词汇英汉对照表Aabsolute error 绝对误差 absolute tolerance 绝对容限 adaptive mesh 适应性网格Bboundary condition 边界条件Ccontour plot 等值线图 converge 收敛 coordinate 坐标系Ddecomposed 分解的 decomposed geometry matrix 分解几何矩阵diagonal matrix 对角矩阵Dirichlet boundary conditions Dirichlet边界条件Eeigenvalue 特征值elliptic 椭圆形的error estimate 误差估计exact solution 精确解Ggeneralized Neumann boundary condition 推广的Neumann 边界条件 geometry 几何形状geometry description matrix 几何描述矩阵 geometry matrix 几何矩阵 graphical user interface（GUI）图形用户界面Hhyperbolic 双曲线的Iinitial mesh 初始网格Jjiggle 微调LLagrange multipliers 拉格朗日乘子Laplace equation 拉普拉斯方程linear interpolation 线性插值 loop 循环Mmachine precision 机器精度 mixed boundary condition 混合边界条件NNeuman boundary condition Neuman边界条件 node point 节点 nonlinear solver 非线性求解器 normal vector 法向量PParabolic 抛物线型的 partial differential equation 偏微分方程plane strain 平面应变 plane stress 平面应力 Poisson's equation 泊松方程 polygon 多边形 positive definite 正定Qquality 质量Rrefined triangular mesh 加密的三角形网格relative tolerance 相对容限 relative tolerance 相对容限 residual 残差 residual norm 残差范数Ssingular 奇异的二、常用的数学英语表述1.Logicthere existfor allp?q p implies q / if p, then qp?q p if and only if q /p is equivalent to q / p and q are equivalent2.Setsx∈A x belongs to A / x is an element (or a member) of Ax?A x does not belong to A / x is not an element (or a member) of AA?B A is contained in B / A is a subset of BA?B A contains B / B is a subset of AA∩B A cap B / A meet B / A intersection BA∪B A cup B / A join B / A union BA\B A minus B / the diference between A and BA×B A cross B / the cartesian product of A and B3. Real numbersx+1 x plus onex-1 x minus onex±1 x plus or minus onexy xy / x multiplied by y(x - y)(x + y) x minus y, x plus yx y x over y= the equals signx = 5 x equals 5 / x is equal to 5x≠5x (is) not equal to 5x≡y x is equivalent to (or identical with) yx ≡ y x is not equivalent to (or identical wit h) yx > y x is greater than yx≥y x is greater than or equal to yx < y x is less than yx≤y x is less than or equal to y0 < x < 1 zero is less than x is less than 10≤x≤1zero is less than or equal to x is less than or equal to 1 | x | mod x / modulus xx 2 x squared / x (raised) to the power 2x 3 x cubedx 4 x to the fourth / x to the power fourx n x to the nth / x to the power nx ?n x to the (power) minus nx (square) root x / the square root of xx 3 cube root (of) xx 4 fourth root (of) xx n nth root (of) x( x+y ) 2 x plus y all squared( x y ) 2 x over y all squaredn! n factorialx ^ x hatx ˉ x barx ?x tildex i xi / x subscript i / x suffix i / x sub i∑ i=1 n a i the sum from i equals one to n a i / the sum as i runs from 1 to n of the a i4. Linear algebra‖ x ‖the norm (or modulus) of xOA →OA / vector OAOA ˉ OA / the length of the segment OAA T A transpose / the transpose of AA ?1 A inverse / the inverse of A5. Functionsf( x ) fx / f of x / the function f of xf:S→T a function f from S to Tx→y x maps to y / x is sent (or mapped) to yf'( x ) f prime x / f dash x / the (first) derivative of f with respect to xf''( x ) f double-prime x / f double-dash x / the second derivative of f with r espect to xf'''( x ) triple-prime x / f triple-dash x / the third derivative of f with respect to xf (4) ( x ) f four x / the fourth derivative of f with respect to xf ? x 1the partial (derivative) of f with respect to x12 f ? x 1 2the second partial (derivative) of f with respect to x1∫ 0 ∞the i ntegral from zero to infinitylim?x→0 the limit as x approaches zerolim?x→0 + the limit as x approaches zero from abovelim?x→0 ?the limit as x approaches zero from belowlog e y log y to the base e / log to the base e of y / natural log (of) yln?y log y to the base e / log to the base e of y / natural log (of) y一般词汇数学mathematics, maths(BrE), math(AmE)公理axiom定理theorem计算calculation运算operation证明prove假设hypothesis, hypotheses(pl.)命题proposition算术arithmetic加plus(prep.), add(v.), addition(n.)被加数augend, summand加数addend和sum减minus(prep.), subtract(v.), subtraction(n.)被减数minuend减数subtrahend差remainder乘times(prep.), multiply(v.), multiplication(n.)被乘数multiplicand, faciend乘数multiplicator积product除divided by(prep.), divide(v.), division(n.)被除数dividend除数divisor商quotient等于equals, is equal to, is equivalent to 大于is greater than 小于is lesser than大于等于is equal or greater than小于等于is equal or lesser than运算符operator数字digit数number自然数natural number整数integer小数decimal小数点decimal point分数fraction分子numerator分母denominator比ratio正positive负negative零null, zero, nought, nil十进制decimal system二进制binary system十六进制hexadecimal system权weight, significance进位carry截尾truncation四舍五入round下舍入round down上舍入round up有效数字significant digit无效数字insignificant digit代数algebra公式formula, formulae(pl.)单项式monomial多项式polynomial, multinomial系数coefficient未知数unknown, x-factor, y-factor, z-factor 等式，方程式equation一次方程simple equation二次方程quadratic equation三次方程cubic equation四次方程quartic equation不等式inequation阶乘factorial对数logarithm指数，幂exponent乘方power二次方，平方square三次方，立方cube四次方the power of four, the fourth power n次方the power of n, the nth power开方evolution, extraction二次方根，平方根square root三次方根，立方根cube root四次方根the root of four, the fourth root n次方根the root of n, the nth root集合aggregate元素element空集void子集subset交集intersection并集union补集complement映射mapping函数function定义域domain, field of definition值域range常量constant变量variable单调性monotonicity奇偶性parity周期性periodicity图象image数列，级数series微积分calculus微分differential导数derivative极限limit无穷大infinite(a.) infinity(n.) 无穷小infinitesimal积分integral定积分definite integral不定积分indefinite integral 有理数rational number无理数irrational number实数real number虚数imaginary number复数complex number矩阵matrix行列式determinant几何geometry点point线line面plane体solid线段segment射线radial平行parallel相交intersect角angle角度degree弧度radian锐角acute angle直角right angle钝角obtuse angle平角straight angle周角perigon底base边side高height三角形triangle锐角三角形acute triangle直角三角形right triangle直角边leg斜边hypotenuse勾股定理Pythagorean theorem钝角三角形obtuse triangle不等边三角形scalene triangle等腰三角形isosceles triangle等边三角形equilateral triangle四边形quadrilateral平行四边形parallelogram矩形rectangle长length宽width附：在一个分数里，分子或分母或两者均含有分数。
概率与统计英语
《概率论与数理统计》基本名词中英文对照表英文中文Probability theory 概率论mathematical statistics 数理统计deterministic phenomenon 确定性现象random phenomenon 随机现象sample space 样本空间random occurrence 随机事件fundamental event 基本事件certain event 必然事件impossible event 不可能事件random test 随机试验incompatible events 互不相容事件frequency 频率classical probabilistic model 古典概型geometric probability 几何概率conditional probability 条件概率multiplication theorem 乘法定理Bayes's formula 贝叶斯公式Prior probability 先验概率Posterior probability 后验概率Independent events 相互独立事件Bernoulli trials 贝努利试验random variable 随机变量probability distribution 概率分布distribution function 分布函数discrete random variable 离散随机变量distribution law 分布律hypergeometric distribution 超几何分布random sampling model 随机抽样模型binomial distribution 二项分布Poisson distribution 泊松分布geometric distribution 几何分布probability density 概率密度continuous random variable 连续随机变量uniformly distribution 均匀分布exponential distribution 指数分布numerical character 数字特征mathematical expectation 数学期望variance 方差moment 矩central moment 中心矩n-dimensional random variable n-维随机变量two-dimensional random variable 二维离散随机变量joint probability distribution 联合概率分布joint distribution law 联合分布律joint distribution function 联合分布函数boundary distribution law 边缘分布律boundary distribution function 边缘分布函数exponential distribution 二维指数分布continuous random variable 二维连续随机变量joint probability density 联合概率密度boundary probability density 边缘概率密度conditional distribution 条件分布conditional distribution law 条件分布律conditional probability density 条件概率密度covariance 协方差dependency coefficient 相关系数normal distribution 正态分布limit theorem 极限定理standard normal distribution 标准正态分布logarithmic normal distribution 对数正态分布covariance matrix 协方差矩阵central limit theorem 中心极限定理Chebyshev's inequality 切比雪夫不等式Bernoulli's law of large numbers 贝努利大数定律statistics 统计量simple random sample 简单随机样本sample distribution function 样本分布函数sample mean 样本均值sample variance 样本方差sample standard deviation 样本标准差sample covariance 样本协方差sample correlation coefficient 样本相关系数order statistics 顺序统计量sample median 样本中位数sample fractiles 样本极差sampling distribution 抽样分布parameter estimation 参数估计estimator 估计量estimate value 估计值unbiased estimator 无偏估计unbiassedness 无偏性biased error 偏差mean square error 均方误差relative efficient 相对有效性minimum variance 最小方差asymptotic unbiased estimator 渐近无偏估计量uniformly estimator 一致性估计量moment method of estimation 矩法估计maximum likelihood method of estimation 极大似然估计法likelihood function 似然函数maximum likelihood estimator 极大似然估计值interval estimation 区间估计hypothesis testing 假设检验statistical hypothesis 统计假设simple hypothesis 简单假设composite hypothesis 复合假设rejection region 拒绝域acceptance domain 接受域test statistics 检验统计量linear regression analysis 线性回归分析1 概率论与数理统计词汇英汉对照表Aabsolute value 绝对值accept 接受acceptable region 接受域additivity 可加性adjusted 调整的alternative hypothesis 对立假设analysis 分析analysis of covariance 协方差分析analysis of variance 方差分析arithmetic mean 算术平均值association 相关性assumption 假设assumption checking 假设检验availability 有效度average 均值Bbalanced 平衡的band 带宽bar chart 条形图beta-distribution 贝塔分布between groups 组间的bias 偏倚binomial distribution 二项分布binomial test 二项检验Ccalculate 计算case 个案category 类别center of gravity 重心central tendency 中心趋势chi-square distribution 卡方分布chi-square test 卡方检验classify 分类cluster analysis 聚类分析coefficient 系数coefficient of correlation 相关系数collinearity 共线性column 列compare 比较comparison 对照components 构成，分量compound 复合的confidence interval 置信区间consistency 一致性constant 常数continuous variable 连续变量control charts 控制图correlation 相关covariance 协方差covariance matrix 协方差矩阵critical point 临界点critical value 临界值crosstab 列联表cubic 三次的，立方的cubic term 三次项cumulative distribution function 累加分布函数curve estimation 曲线估计Ddata 数据default 默认的definition 定义deleted residual 剔除残差density function 密度函数dependent variable 因变量description 描述design of experiment 试验设计deviations 差异df.(degree of freedom) 自由度diagnostic 诊断dimension 维discrete variable 离散变量discriminant function 判别函数discriminatory analysis 判别分析distance 距离distribution 分布D-optimal design D-优化设计Eeaqual 相等effects of interaction 交互效应efficiency 有效性eigenvalue 特征值equal size 等含量equation 方程error 误差estimate 估计estimation of parameters 参数估计estimations 估计量evaluate 衡量exact value 精确值expectation 期望expected value 期望值exponential 指数的exponential distributon 指数分布extreme value 极值Ffactor 因素，因子factor analysis 因子分析factor score 因子得分factorial designs 析因设计factorial experiment 析因试验fit 拟合fitted line 拟合线fitted value 拟合值fixed model 固定模型fixed variable 固定变量fractional factorial design 部分析因设计frequency 频数F-test F检验full factorial design 完全析因设计function 函数Ggamma distribution 伽玛分布geometric mean 几何均值group 组Hharmomic mean 调和均值heterogeneity 不齐性histogram 直方图homogeneity 齐性homogeneity of variance 方差齐性hypothesis 假设hypothesis test 假设检验Iindependence 独立independent variable 自变量independent-samples 独立样本index 指数index of correlation 相关指数interaction 交互作用interclass correlation 组内相关interval estimate 区间估计intraclass correlation 组间相关inverse 倒数的iterate 迭代Kkernal 核Kolmogorov-Smirnov test柯尔莫哥洛夫-斯米诺夫检验kurtosis 峰度Llarge sample problem 大样本问题layer 层least-significant difference 最小显著差数least-square estimation 最小二乘估计least-square method 最小二乘法level 水平level of significance 显著性水平leverage value 中心化杠杆值life 寿命life test 寿命试验likelihood function 似然函数likelihood ratio test 似然比检验linear 线性的linear estimator 线性估计linear model 线性模型linear regression 线性回归linear relation 线性关系linear term 线性项logarithmic 对数的logarithms 对数logistic 逻辑的lost function 损失函数Mmain effect 主效应matrix 矩阵maximum 最大值maximum likelihood estimation 极大似然估计mean squared deviation(MSD) 均方差mean sum of square 均方和measure 衡量media 中位数M-estimator M估计minimum 最小值missing values 缺失值mixed model 混合模型mode 众数model 模型Monte Carle method 蒙特卡罗法moving average 移动平均值multicollinearity 多元共线性multiple comparison 多重比较multiple correlation 多重相关multiple correlation coefficient 复相关系数multiple correlation coefficient 多元相关系数multiple regression analysis 多元回归分析multiple regression equation 多元回归方程multiple response 多响应multivariate analysis 多元分析Nnegative relationship 负相关nonadditively 不可加性nonlinear 非线性nonlinear regression 非线性回归noparametric tests 非参数检验normal distribution 正态分布null hypothesis 零假设number of cases 个案数Oone-sample 单样本one-tailed test 单侧检验one-way ANOVA 单向方差分析one-way classification 单向分类optimal 优化的optimum allocation 最优配制order 排序order statistics 次序统计量origin 原点orthogonal 正交的outliers 异常值Ppaired observations 成对观测数据paired-sample 成对样本parameter 参数parameter estimation 参数估计partial correlation 偏相关partial correlation coefficient 偏相关系数partial regression coefficient 偏回归系数percent 百分数percentiles 百分位数pie chart 饼图point estimate 点估计poisson distribution 泊松分布polynomial curve 多项式曲线polynomial regression 多项式回归polynomials 多项式positive relationship 正相关power 幂P-P plot P-P概率图predict 预测predicted value 预测值prediction intervals 预测区间principal component analysis 主成分分析proability 概率probability density function 概率密度函数probit analysis 概率分析proportion 比例Qqadratic 二次的Q-Q plot Q-Q概率图quadratic term 二次项quality control 质量控制quantitative 数量的，度量的quartiles 四分位数Rrandom 随机的random number 随机数random number 随机数random sampling 随机取样random seed 随机数种子random variable 随机变量randomization 随机化range 极差rank 秩rank correlation 秩相关rank statistic 秩统计量regression analysis 回归分析regression coefficient 回归系数regression line 回归线reject 拒绝rejection region 拒绝域relationship 关系reliability 可靠性repeated 重复的report 报告，报表residual 残差residual sum of squares 剩余平方和response 响应risk function 风险函数robustness 稳健性root mean square 标准差row 行run 游程run test 游程检验Ssample 样本sample size 样本容量sample space 样本空间sampling 取样sampling inspection 抽样检验scatter chart 散点图S-curve S形曲线separately 单独地sets 集合sign test 符号检验significance 显著性significance level 显著性水平significance testing 显著性检验significant 显著的，有效的significant digits 有效数字skewed distribution 偏态分布skewness 偏度small sample problem 小样本问题smooth 平滑sort 排序soruces of variation 方差来源space 空间spread 扩展square 平方standard deviation 标准离差standard error of mean 均值的标准误差standardization 标准化standardize 标准化statistic 统计量statistical quality control 统计质量控制std. residual 标准残差stepwise regression analysis 逐步回归stimulus 刺激strong assumption 强假设stud. deleted residual 学生化剔除残差stud. residual 学生化残差subsamples 次级样本sufficient statistic 充分统计量sum 和sum of squares 平方和summary 概括，综述Ttable 表t-distribution t分布test 检验test criterion 检验判据test for linearity 线性检验test of goodness of fit 拟合优度检验test of homogeneity 齐性检验test of independence 独立性检验test rules 检验法则test statistics 检验统计量testing function 检验函数time series 时间序列tolerance limits 容许限total 总共，和transformation 转换treatment 处理trimmed mean 截尾均值true value 真值t-test t检验two-tailed test 双侧检验Uunbalanced 不平衡的unbiased estimation 无偏估计unbiasedness 无偏性uniform distribution 均匀分布Vvalue of estimator 估计值variable 变量variance 方差variance components 方差分量variance ratio 方差比various 不同的vector 向量Wweight 加权，权重weighted average 加权平均值within groups 组内的ZZ score Z分数。
计量经济学词汇
Population 总体Sample 样本Random variable(r.v) 随机变量Discrete 离散的Pdf : probability density functionCdf：cumulative distribution function Independent 独立Iff: if and only ifVice versa 反之亦然standard deviation 标准差covariance 协方差correlation coefficient 相关系数expected value（population means）期望OLS estimator 最小二乘估计量regression coefficients 回归系数intercept term 截距项beta0slope parameter 斜率项beta1rerror term 误差项upopulation regression function 总体回归方程SRF 样本回归方程moment 矩residual 残差tabulate(stata) 制成表格dotplot（stata）histogram（stata）制成柱状图graph box（stata）sample variance of y. y的样本方差（SST/n-1）variation 变异fitted value 样本的拟和值y-hatgoodness of fit 拟和优度cross-sectional截面数据constant elasticity model 常熟弹性模型unbiasedness 无偏性Homoskedasticity 同方差性Heteroskedastic 异方差性Standard error 标准误Se（beta）：beta的标准误Sd（beta）：beta的标准差=sqrt（SSR/n-2）回归标准误Partialling effect 局部效应ceteris paribus 其他情况相同omitted variable 遗失变量Multicollinearity 多重共线性最优线性无偏估计量（BLUE）asymptotic distribution 渐进分布MLR.1 –MLR.6 ：CLM 经典线性模型假设null hypothesis 零假设critical value 临界值significance level显著性水平jointly significant 联合显著Confidence Intervals 置信区间Consistency 一致性Asymptotic Efficiency 渐进有效。
统计学专业英语词汇汇总
统计学复试专业词汇汇总population 总体sampling unit 抽样单元sample 样本observed value 观测值descriptive statistics 描述性统计量random sample 随机样本simple random sample 简单随机样本statistics 统计量order statistic 次序统计量sample range 样本极差mid-range 中程数estimator 估计量sample median 样本中位数sample moment of order k k阶样本矩sample mean 样本均值average 平均数arithmetic mean 算数平均值sample variance 样本方差sample standard deviation 样本标准差sample coefficient of variation 样本变异系数standardized sample random variable 标准化样本随机变量sample coefficient of skewness （歪斜）样本偏度系数sample coefficient of kurtosis (峰态) 样本峰度系数sample covariance 样本协方差sample correclation coefficient 样本相关系数standard error 标准误差interval estimator 区间估计statistical tolerance interval 统计容忍区间statistical tolerance limit 统计容忍限confidence interval 置信区间one-sided confidence interval 单侧置信区间prediction interval 预测区间estimate 估计值error of estimation 估计误差bias 偏倚unbiased estimator 无偏估计量maximum likelihood estimator 极大似然估计量estimation 估计maximum likelihood estimation 极大似然估计likelihood function 似然函数profile likelihood funtion 剖面函数hypothesis 假设null hypothesis 原假设alternative hypothesis 备择假设simple hypothesis 简单假设composite hypothesis 复合假设significance level 显著性水平type I error 第一类错误type II error 第二类错误statistical test 统计检验significance test 显著性检验p-value p值power of a test 检验功效power curve 功效曲线test statistic 检验统计量graphical descriptive statistics 图形描述性统计量numerical descriptive statistics 数值描述性统计量classes 类（组）class 类class 组class limits; class boundaries 组限mid-point of class 组中值class width 组距frequency 频数frequency distribution 频数分布histogram 直方图bar chart 条形图cumulative frequency 累积频数relative frequency 频率cumulative relative frequency 累积频率sample space 样本空间event 事件complementary event 对立事件independent events 独立事件probability [of an event A] [事件A的]概率conditional probability 条件概率distribution function [of a random variable X] [随机变量X的]分布函数family of distributions 分布族parameter 参数random variable 随机变量probability distribution 概率分布distribution 分布expectation 期望p-quantile; p-fractile p分位数median 中位数quartile 四分位数univariate probability distribution 一维概率分布univariate distribution 一维分布multivariate probability distribution 多维概率分布multivariate distribution 多维分布marginal probability distrubition 边缘概率分布marginal distribution 边缘分布conditional probability distribution 条件概率分布conditional distribution 条件分布regression curve 回归曲线regression surface 回归曲面discrete probability distribution 离散概率分布discrete distribution 离散分布continuous probability distribution 连续概率分布continuous distribution 连续分布probability [mass] function 概率函数mode of probability [mass] function 概率函数的众数probability density function 概率密度函数mode of probability density function 概率密度函数的众数discrete random variable 离散随机变量continuous random variable 连续随机变量centred probability distribution 中心化概率分布centred random variable 中心化随机变量standardized probability distribution 标准化概率分布standardized random variable 标准化随机变量moment of order r r阶[原点]矩means 均值moment of order r = 1 一阶矩mean 均值variance 方差standard deviation 标准差coefficient of variation 变异系数coefficient of skewness 偏度系数coefficient of kurtosis 峰度系数joint moment of order r and s (r,s)阶联合[原点]矩joint central moment of order r and s (r,s)阶联合中心矩covariance 协方差correlation coefficient 相关系数multinomial distribution 多项分布binomial distribution 二项分布Poisson distribution 泊松分布hypergeometric distibution 超几何分布negative binomial distribution 负二项分布normal distribution, Gaussian distribution 正态分布standard normal distribution, standard Gaussian distribution 标准正态分布lognormal distribution 对数正态分布t distribution; Student's distribution t分布degrees of freedom 自由度F distribution F分布gamma distribution 伽玛分布, Γ分布chi-squared distribution 卡方分布,χ2分布exponential distribution 指数分布beta distribution 贝塔分布,β分布uniform distribution, rectangular distribution 均匀分布type I value distribution; Gumbel distribution I型极值分布type II value distribution; Gumbel distribution II型极值分布Weibull distribution 威布尔分布type III value distribution; Gumbel distribution III型极值分布multivariate normal distribution 多维正态分布bivariate normal distribution 二维正态分布standard bivariate normal distribution 标准二维正态分布sampling distribution 抽样分布probability space 概率空间。
概率统计c 4_2
The pdf for a uniform distribution Figure 4.6 6
Example 6
cont’d
For x < A, F(x) = 0, since there is no area under the graph of the density function to the left of such an x. For x B, F(x) = 1, since all the area is accumulated to the left of such an x. Finally for A x B,
Similarly, the 40th percentile is the score that exceeds 40% of all scores.
20
Percentiles of a Continuous Distribution
Proposition Let p be a number between 0 and 1. The (100p)th percentile of the distribution of a continuous rv X, denoted by (p), is defined by
For each x, F(x) is the area under the density curve to the left of x. This is illustrated in Figure 4.5, where F(x) increases smoothly as x increases.
16
Example 7
Suppose the pdf of the magnitude X of a dynamic load on a bridge (in newtons) is
§2.1 随机变量的概念与离散型随机变量§2.2 随机变量的分布函数(distribution function)
解 由概率分布的性质得
1 . 得 15a = 1, 即 a 15
p
i 1
5
i
1
第2章
§2.1-2.2 随机变量的概念, 分布函数
第11页
课堂练习2 在一个袋子中有10个球，其中6个白球，4 个红球。从中任取3个，求抽到红球数的概率分布。 解 用X表示抽到的红球数，则X所有可能的取值为0，1，2，3。
Ω={ t | t ≥ 0}
第2章
§2.1-2.2 随机变量的概念, 分布函数
第4页
定义 设随机试验E的样本空间为Ω，如果对于每一个 ω∈Ω，都有唯一的一个实数X(ω)与之对应，则称 X(ω)为随机变量，并简记为X。
注意： 1. X是定义在Ω上的实值、单值函数。 2. 若给定了试验的样本空间的概率分布。就可以确 定随机变量 X 取某些值时的概率，设 A 为一实数集,
第2章
§2.1-2.2 随机变量的概念, 分布函数
第2页
例1续 掷一枚硬币10次，观察出现正面的次数。
此时，试验的样本空间是由一系列长度为10的正反面 的序列组成，总共有 210 个元素。 定义函数 X 如下：对任意一个序列
,
定义
X ( ) 出现正面的次数。
这样的定义的函数 X 是一个随机变量。它反映了出 现正面的次数。利用它可以很容易的描述随机事件。 例如， {X≤5}= 出现正面次数不多于5次的事件.
第2章
§2.1-2.2 随机变量的概念, 分布函数
第9页
定义 设离散型随机变量X所有可能的取值为 x1 , x2 , … , xn , … X取各个值的概率，即事件{X=xi}的概率为 P { X = xi } = pi （i = 1, 2, …） 则称之为离散型随机变量X的概率分布或分布列(律). 亦可用下面的概率分布表来表示
中级计量经济学讲义_第二章第一节分布函数(Distribution function),数学期望(Expectation)
上课材料之三：第二节 分布函数(Distribution function)，数学期望(Expectation)与方差(Variance)本节主要介绍概率及其分布函数，数学期望，方差等方面的基础知识。
一、概率(Probability)1、概率定义(Definition of Probability)在自然界和人类社会中有着两类不同的现象，一类是决定性现象，其特征是在一定条件必然会发生的现象；另一类是随机现象，其特征是在基本条件不变的情况下，观察到或试验的结果会不同。
换句话说，就个别的试验或观察而言，它会时而出现这种结果，时而出现那样结果，呈现出一种偶然情况，这种现象称为随机现象。
随机现象有其偶然性的一面，也有其必然性的一面，这种必然性表现为大量试验中随机事件出现的频率的稳定性，即一个随机事件出现的频率常在某了固定的常数附近变动，这种规律性我们称之为统计规律性。
频率的稳定性说明随机事件发生可能性大小是随机事件本身固定的，不随人们意志而改变的一种客观属性，因此可以对它进行度量。
对于一个随机事件A ，用一个数P （A ）来表示该事件发生的可能性大小，这个数P （A ）就称为随机事件A 的概率，因此，概率度量了随机事件发生的可能性的大小。
对于随机现象，光知道它可能出现什么结果，价值不大，而指出各种结果出现的可能性的大小则具有很大的意义。
有了概率的概念，就使我们能对随机现象进行定量研究，由此建立了一个新的数学分支——概率论。
概率的定义定义在事件域F 上的一个集合函数P 称为概率，如果它满足如下三个条件： （i ）P （A ）≥0，对一切∈A F （ii ）P （Ω）=1；（iii ）若∈i A ，i=1,2…，且两两互不相容，则∑∑∞=∞==⎪⎭⎫ ⎝⎛11)(i ii i AP A P性质（iii ）称为可列可加性（conformable addition ）或完全可加性。
推论1：对任何事件A 有)(1)(A P A P -=；推论2：不可能事件的概率为0，即0)(=φP ； 推论3：)()()()(AB P B P A P B A P -+=⋃。
统计学专业英语词汇
概率论与数理统计词汇英汉对照表Aabsolute value 绝对值accept 接受acceptable region 接受域additivity 可加性adjusted 调整的alternative hypothesis 对立假设analysis 分析analysis of covariance 协方差分析analysis of variance 方差分析arithmetic mean 算术平均值association 相关性assumption 假设assumption checking 假设检验availability 有效度average 均值Bbalanced 平衡的band 带宽bar chart 条形图beta-distribution 贝塔分布between groups 组间的bias 偏倚binomial distribution 二项分布binomial test 二项检验Ccalculate 计算case 个案category 类别center of gravity 重心central tendency 中心趋势chi-square distribution 卡方分布chi-square test 卡方检验classify 分类cluster analysis 聚类分析coefficient 系数coefficient of correlation 相关系数collinearity 共线性column 列compare 比较comparison 对照components 构成，分量compound 复合的confidence interval 置信区间consistency 一致性constant 常数continuous variable 连续变量control charts 控制图correlation 相关covariance 协方差covariance matrix 协方差矩阵critical point 临界点critical value 临界值crosstab 列联表cubic 三次的，立方的cubic term 三次项cumulative distribution function 累加分布函数curve estimation 曲线估计Ddata 数据default 默认的definition 定义deleted residual 剔除残差density function 密度函数dependent variable 因变量description 描述design of experiment 试验设计deviations 差异df.(degree of freedom) 自由度diagnostic 诊断dimension 维discrete variable 离散变量discriminant function 判别函数discriminatory analysis 判别分析distance 距离distribution 分布D-optimal design D-优化设计Eeaqual 相等effects of interaction 交互效应efficiency 有效性eigenvalue 特征值equal size 等含量equation 方程error 误差estimate 估计estimation of parameters 参数估计estimations 估计量evaluate 衡量exact value 精确值expectation 期望expected value 期望值exponential 指数的exponential distributon 指数分布extreme value 极值Ffactor 因素，因子factor analysis 因子分析factor score 因子得分factorial designs 析因设计factorial experiment 析因试验fit 拟合fitted line 拟合线fitted value 拟合值fixed model 固定模型fixed variable 固定变量fractional factorial design 部分析因设计frequency 频数F-test F检验full factorial design 完全析因设计function 函数Ggamma distribution 伽玛分布geometric mean 几何均值group 组Hharmomic mean 调和均值heterogeneity 不齐性histogram 直方图homogeneity 齐性homogeneity of variance 方差齐性hypothesis 假设hypothesis test 假设检验Iindependence 独立independent variable 自变量independent-samples 独立样本index 指数index of correlation 相关指数interaction 交互作用interclass correlation 组内相关interval estimate 区间估计intraclass correlation 组间相关inverse 倒数的iterate 迭代Kkernal 核Kolmogorov-Smirnov test柯尔莫哥洛夫-斯米诺夫检验kurtosis 峰度Llarge sample problem 大样本问题layer 层least-significant difference 最小显著差数least-square estimation 最小二乘估计least-square method 最小二乘法level 水平level of significance 显著性水平leverage value 中心化杠杆值life 寿命life test 寿命试验likelihood function 似然函数likelihood ratio test 似然比检验linear 线性的linear estimator 线性估计linear model 线性模型linear regression 线性回归linear relation 线性关系linear term 线性项logarithmic 对数的logarithms 对数logistic 逻辑的lost function 损失函数Mmain effect 主效应matrix 矩阵maximum 最大值maximum likelihood estimation 极大似然估计mean squared deviation(MSD) 均方差mean sum of square 均方和measure 衡量media 中位数M-estimator M估计minimum 最小值missing values 缺失值mixed model 混合模型mode 众数model 模型Monte Carle method 蒙特卡罗法moving average 移动平均值multicollinearity 多元共线性multiple comparison 多重比较multiple correlation 多重相关multiple correlation coefficient 复相关系数multiple correlation coefficient 多元相关系数multiple regression analysis 多元回归分析multiple regression equation 多元回归方程multiple response 多响应multivariate analysis 多元分析Nnegative relationship 负相关nonadditively 不可加性nonlinear 非线性nonlinear regression 非线性回归noparametric tests 非参数检验normal distribution 正态分布null hypothesis 零假设number of cases 个案数Oone-sample 单样本one-tailed test 单侧检验one-way ANOVA 单向方差分析one-way classification 单向分类optimal 优化的optimum allocation 最优配制order 排序order statistics 次序统计量origin 原点orthogonal 正交的outliers 异常值Ppaired observations 成对观测数据paired-sample 成对样本parameter 参数parameter estimation 参数估计partial correlation 偏相关partial correlation coefficient 偏相关系数partial regression coefficient 偏回归系数percent 百分数percentiles 百分位数pie chart 饼图point estimate 点估计poisson distribution 泊松分布polynomial curve 多项式曲线polynomial regression 多项式回归polynomials 多项式positive relationship 正相关power 幂P-P plot P-P概率图predict 预测predicted value 预测值prediction intervals 预测区间principal component analysis 主成分分析proability 概率probability density function 概率密度函数probit analysis 概率分析proportion 比例Qqadratic 二次的Q-Q plot Q-Q概率图quadratic term 二次项quality control 质量控制quantitative 数量的，度量的quartiles 四分位数Rrandom 随机的random number 随机数random number 随机数random sampling 随机取样random seed 随机数种子random variable 随机变量randomization 随机化range 极差rank 秩rank correlation 秩相关rank statistic 秩统计量regression analysis 回归分析regression coefficient 回归系数regression line 回归线reject 拒绝rejection region 拒绝域relationship 关系reliability 可靠性repeated 重复的report 报告，报表residual 残差residual sum of squares 剩余平方和response 响应risk function 风险函数robustness 稳健性root mean square 标准差row 行run 游程run test 游程检验Ssample 样本sample size 样本容量sample space 样本空间sampling 取样sampling inspection 抽样检验scatter chart 散点图S-curve S形曲线separately 单独地sets 集合sign test 符号检验significance 显著性significance level 显著性水平significance testing 显著性检验significant 显著的，有效的significant digits 有效数字skewed distribution 偏态分布skewness 偏度small sample problem 小样本问题smooth 平滑sort 排序soruces of variation 方差来源space 空间spread 扩展square 平方standard deviation 标准离差standard error of mean 均值的标准误差standardization 标准化standardize 标准化statistic 统计量statistical quality control 统计质量控制std. residual 标准残差stepwise regression analysis 逐步回归stimulus 刺激strong assumption 强假设stud. deleted residual 学生化剔除残差stud. residual 学生化残差subsamples 次级样本sufficient statistic 充分统计量sum 和sum of squares 平方和summary 概括，综述Ttable 表t-distribution t分布test 检验test criterion 检验判据test for linearity 线性检验test of goodness of fit 拟合优度检验test of homogeneity 齐性检验test of independence 独立性检验test rules 检验法则test statistics 检验统计量testing function 检验函数time series 时间序列tolerance limits 容许限total 总共，和transformation 转换treatment 处理trimmed mean 截尾均值true value 真值t-test t检验two-tailed test 双侧检验Uunbalanced 不平衡的unbiased estimation 无偏估计unbiasedness 无偏性uniform distribution 均匀分布Vvalue of estimator 估计值variable 变量variance 方差variance components 方差分量variance ratio 方差比various 不同的vector 向量Wweight 加权，权重weighted average 加权平均值within groups 组内的ZZ score Z分数最优化方法词汇英汉对照表Aactive constraint 活动约束active set method 活动集法analytic gradient 解析梯度approximate 近似arbitrary 强制性的argument 变量attainment factor 达到因子Bbandwidth 带宽be equivalent to 等价于best-fit 最佳拟合bound 边界Ccoefficient 系数complex-value 复数值component 分量constant 常数constrained 有约束的constraint 约束constraint function 约束函数continuous 连续的converge 收敛cubic polynomial interpolation method 三次多项式插值法curve-fitting 曲线拟合Ddata-fitting 数据拟合default 默认的，默认的define 定义diagonal 对角的direct search method 直接搜索法direction of search 搜索方向discontinuous 不连续Eeigenvalue 特征值empty matrix 空矩阵equality 等式exceeded 溢出的Ffeasible 可行的feasible solution 可行解finite-difference 有限差分first-order 一阶GGauss-Newton method 高斯-牛顿法goal attainment problem 目标达到问题gradient 梯度gradient method 梯度法Hhandle 句柄Hessian matrix 海色矩阵Iindependent variables 独立变量inequality 不等式infeasibility 不可行性infeasible 不可行的initial feasible solution 初始可行解initialize 初始化inverse 逆invoke 激活iteration 迭代iteration 迭代JJacobian 雅可比矩阵LLagrange multiplier 拉格朗日乘子large-scale 大型的least square 最小二乘least squares sense 最小二乘意义上的Levenberg-Marquardt method列文伯格-马夸尔特法line search 一维搜索linear 线性的linear equality constraints 线性等式约束linear programming problem 线性规划问题local solution 局部解Mmedium-scale 中型的minimize 最小化mixed quadratic and cubic polynomial interpolation and extrapolation method 混合二次、三次多项式内插、外插法multiobjective 多目标的Nnonlinear 非线性的norm 范数Oobjective function 目标函数observed data 测量数据optimization routine 优化过程optimize 优化optimizer 求解器over-determined system 超定系统Pparameter 参数partial derivatives 偏导数polynomial interpolation method多项式插值法Qquadratic 二次的quadratic interpolation method 二次内插法quadratic programming 二次规划Rreal-value 实数值residuals 残差robust 稳健的robustness 稳健性，鲁棒性Sscalar 标量semi-infinitely problem 半无限问题Sequential Quadratic Programming method序列二次规划法simplex search method 单纯形法solution 解sparse matrix 稀疏矩阵sparsity pattern 稀疏模式sparsity structure 稀疏结构starting point 初始点step length 步长subspace trust region method 子空间置信域法sum-of-squares 平方和symmetric matrix 对称矩阵Ttermination message 终止信息termination tolerance 终止容限the exit condition 退出条件the method of steepest descent 最速下降法transpose 转置Uunconstrained 无约束的under-determined system 负定系统Vvariable 变量vector 矢量Wweighting matrix 加权矩阵样条词汇英汉对照表Aapproximation 逼近array 数组a spline in b-form/b-spline b样条a spline of polynomial piece /ppform spline分段多项式样条Bbivariate spline function 二元样条函数break/breaks 断点coefficient/coefficients 系数cubic interpolation 三次插值/三次内插cubic polynomial 三次多项式cubic smoothing spline 三次平滑样条cubic spline 三次样条cubic spline interpolation三次样条插值/三次样条内插curve 曲线Ddegree of freedom 自由度dimension 维数Eend conditions 约束条件Iinput argument 输入参数interpolation 插值/内插interval 取值区间Kknot/knots 节点Lleast-squares approximation 最小二乘拟合Mmultiplicity 重次multivariate function 多元函数Ooptional argument 可选参数order 阶次output argument 输出参数Ppoint/points 数据点Rrational spline 有理样条rounding error 舍入误差（相对误差）Sscalar 标量sequence 数列（数组）spline 样条spline approximation 样条逼近/样条拟合spline function 样条函数spline curve 样条曲线spline interpolation 样条插值/样条内插spline surface 样条曲面smoothing spline 平滑样条Ttolerance 允许精度Uunivariate function 一元函数Vvector 向量Wweight/weights 权重4 偏微分方程数值解词汇英汉对照表Aabsolute error 绝对误差absolute tolerance 绝对容限adaptive mesh 适应性网格Bboundary condition 边界条件Ccontour plot 等值线图converge 收敛coordinate 坐标系Ddecomposed 分解的decomposed geometry matrix 分解几何矩阵diagonal matrix 对角矩阵Dirichlet boundary conditionsDirichlet边界条件Eeigenvalue 特征值elliptic 椭圆形的error estimate 误差估计exact solution 精确解Ggeneralized Neumann boundary condition推广的Neumann边界条件geometry 几何形状geometry description matrix 几何描述矩阵geometry matrix 几何矩阵graphical user interface（GUI）图形用户界面Hhyperbolic 双曲线的Iinitial mesh 初始网格Jjiggle 微调LLagrange multipliers 拉格朗日乘子Laplace equation 拉普拉斯方程linear interpolation 线性插值loop 循环Mmachine precision 机器精度mixed boundary condition 混合边界条件NNeuman boundary condition Neuman边界条件node point 节点nonlinear solver 非线性求解器normal vector 法向量PParabolic 抛物线型的partial differential equation 偏微分方程plane strain 平面应变plane stress 平面应力Poisson's equation 泊松方程polygon 多边形positive definite 正定Qquality 质量Rrefined triangular mesh 加密的三角形网格relative tolerance 相对容限relative tolerance 相对容限residual 残差residual norm 残差范数Ssingular 奇异的。
概率统计 中英术语对照表
概率统计中英术语对照表Probability Theory概率论Trial 试验intersection交union 并frequency 频率difference 差additivity 可加性complementation 对立contain 包含equivalent 等价mean 均值convolution ［,kɔnvə’lu:ʃən］卷积variance 方差covariance 协方差correlated 相关standard deviation 标准差Random experiment 随机试验random event 随机事件certain event 必然事件impossible event 不可能事件elementary/fundamental event 基本事件the probability of event A 事件的概率sample point 样本点sample space 样本空间Classical probability 古典概型geometric probability 几何概型conditional probability 条件概型total probability 全概率formula of multiplication 乘法公式pair wise independence 两两相互独立Distribution function 分布函数discrete random variable 离散型随机变量two-point distribution （0-1）分布binomial distribution 二次分布Poisson distribution 泊松分布hyper geometric distribution 超几何分布Continuous random variable 连续型随机变量probability density function 概率密度函数uniform distribution 均匀分布Exponential distribution 指数分布standard normal distribution 标准正态分布Cauchy distribution 柯西分布n—dimensional random vector n维随机变量bivariate random variable [bai’vεəriət］二维随机变量joint distribution function 联合分布函数bivariate discrete random variable 二维离散型随机变量joint distribution law 联合分布律bivariate continuous random variable 二维连续型随机变量joint probability density function 联合概率密度函数bivariate normal distribution 二维正态分布marginal distribution function 边缘分布函数marginal distribution law 边缘分布律marginal probability density function 边缘概率密度函数conditional distribution function 条件分布函数conditional probability density function 条件概率密度函数mathematical expectation 数学期望standard random variable 标准随机变量moment generating function 矩母函数characteristic function 特征函数positive correlated 正相关mixed moment 混合矩negative correlated 负相关mixed central moment 混合中心矩moment of order k about the origin 阶原点矩central moment of order k 阶中心矩covariance matrix 协方差矩阵convergence in probability 依概率收敛Bernouli large numbers law 伯努力大数定律Mathematical statistics数理统计individuality 个体population 总体sample size 样本大小simple random sample 随机样本efficiency有效statistic 统计量sample mean 样本均值sample variance样本方差sample standard deviation 样本标准差sample central moment of order k样本的阶中心矩skewness ［’skju:nis］偏度coefficient of variation 变异系数order statistics 次序统计量degrees or freedom 自由度sampling distribution 抽样分布parameter estimation 参数估计point estimation 点估计estimator 估计量estimate 估计值likelihood function 似然函数method of moment 矩估计法unbiased estimator 无偏估计量maximum likelihood estimate 最大似然估计system of likelihood equations似然方程组consistent estimator 一致估计量confidence level 置信水平confidence interval 置信区间upper confidence limit 置信上限parametric hypothesis 参数估计non-parametric hypothesis 非参数估计alternative hypothesis 备择假设null hypothesis 零假设Significance level 显著性水平rejection region 拒绝域acceptance region 接受域test for goodness of fit 拟和优度检验contingency table 列连表regression function 回归函数regression equation 回归方程linear regression model 线形回归模型regression coefficient 回归系数normal linear model 正态线形模型least squares estimate 最小二乘估计method of least squares 最小二乘法sum of squares of residual 残差平方和sum of squares of regression 回归平方和sum of residual 剩余平方和total sum of squares of deviations 总变差平方和coefficient of determination 判定系数point interval 点预测prediction interval 预测区间one—way analysis variance 单因素方差分析two—way analysis of variance 双因素方差分析interaction effect 交互效应。
经验分布函数_概述说明以及解释
经验分布函数概述说明以及解释1. 引言1.1 概述经验分布函数是一种统计工具，用于描述和分析随机变量的分布情况。
它是一种非参数的方法，不需要对概率分布进行假设，因此被广泛应用于各个领域的数据分析中。
通过经验分布函数，我们可以了解到样本数据的累积概率分布，并将其与理论概率分布进行比较。
1.2 文章结构本文将以以下方式呈现关于经验分布函数的研究内容：首先，在第二部分中，我们将对经验分布函数的定义进行详细解释，包括相关的理论介绍、数学表达式以及直观解释。
然后，在第三部分中，我们将探讨经验分布函数在不同领域中的应用场景，例如数据分析与可视化、生物统计学和工程领域等。
接着，在第四部分中，我们将介绍经验分布函数的计算方法和算法实现。
这包括基本思想与步骤、常见的计算方法和公式推导以及算法实现和代码示例。
最后，在第五部分中，我们将给出总结主要观点和研究结果，并对经验分布函数未来发展提出展望和建议。
1.3 目的本文的目的是为读者提供对经验分布函数的全面理解。
通过详细介绍经验分布函数的定义、应用场景以及计算方法，希望能够帮助读者更好地应用经验分布函数进行数据分析，并为未来经验分布函数在各个领域中的发展提供一些启示和建议。
2. 经验分布函数的定义:2.1 理论介绍:经验分布函数是统计学中常用的一种非参数估计方法，用于描述一个随机变量的累积分布函数（CDF）。
该函数基于观测数据样本，通过对每个观测值的累计概率进行排序和求和得到。
它能够直观地展示数据集中数值的分布情况。
2.2 数学表达式:假设我们有一个由n个独立随机观测值组成的样本集合X={x₁, x₂,..., xn}，其中每个xi代表一个随机变量。
经验分布函数F(x)在某个特定点x处的取值表示小于或等于x的样本比例。
数学上，经验分布函数可以表示为：F(x) = (1/n) * Σ(i=1 to n) [I(xi ≤x)]其中[ ]表示指示函数，当括号内条件满足时取值为1，否则为0；Σ表示求和运算；i代表索引变量。
第二节分布函数(Distributionfunction),数学期望(Expectation(金融计量-浙大蒋岳祥))
上课材料之三：第二节 分布函数(Distribution function)，数学期望(Expectation)与方差(Variance)本节主要介绍概率及其分布函数，数学期望，方差等方面的基础知识。
一、概率(Probability)1、概率定义(Definition of Probability)在自然界和人类社会中有着两类不同的现象，一类是决定性现象，其特征是在一定条件必然会发生的现象；另一类是随机现象，其特征是在基本条件不变的情况下，观察到或试验的结果会不同。
换句话说，就个别的试验或观察而言，它会时而出现这种结果，时而出现那样结果，呈现出一种偶然情况，这种现象称为随机现象。
随机现象有其偶然性的一面，也有其必然性的一面，这种必然性表现为大量试验中随机事件出现的频率的稳定性，即一个随机事件出现的频率常在某了固定的常数附近变动，这种规律性我们称之为统计规律性。
频率的稳定性说明随机事件发生可能性大小是随机事件本身固定的，不随人们意志而改变的一种客观属性，因此可以对它进行度量。
对于一个随机事件A ，用一个数P （A ）来表示该事件发生的可能性大小，这个数P （A ）就称为随机事件A 的概率，因此，概率度量了随机事件发生的可能性的大小。
对于随机现象，光知道它可能出现什么结果，价值不大，而指出各种结果出现的可能性的大小则具有很大的意义。
有了概率的概念，就使我们能对随机现象进行定量研究，由此建立了一个新的数学分支——概率论。
概率的定义定义在事件域F 上的一个集合函数P 称为概率，如果它满足如下三个条件： （i ）P （A ）≥0，对一切∈A F （ii ）P （Ω）=1；（iii ）若∈i A ，i=1,2…，且两两互不相容，则∑∑∞=∞==⎪⎭⎫ ⎝⎛11)(i i i i A P A P 性质（iii ）称为可列可加性（conformable addition ）或完全可加性。
推论1：对任何事件A 有)(1)(A P A P -=；推论2：不可能事件的概率为0，即0)(=φP ； 推论3：)()()()(AB P B P A P B A P -+=⋃。
概率论与数理统计(英文)第三章
3. Random Variables3.1 Definition of Random VariablesIn engineering or scientific problems, we are not only interested in the probability of events, but also interested in some variables depending on sample points. （定义在样本点上的变量）For example, we maybe interested in the life of bulbs produced by a certain company, or the weight of cows in a certain farm, etc. These ideas lead to the definition of random variables.1. random variable definitionHere are some examples.Example 3.1.1 A fair die is tossed. The number X shown is a random variable, it takes values in the set {1,2,6}.Example 3.1.2The life t of a bulb selected at random from bulbs produced by company A is a random variable, it takes values in the interval (0,) .Since the outcomes of a random experiment can not be predicted in advance, the exact value of a random variable can not be predicted before the experiment, we can only discuss the probability that it takes somevalue or the values in some subset of R.2. Distribution functionNote The distribution function ()F X is defined on real numbers, not on sample space.Example 3.1.3Let X be the number we get from tossing a fair die. Then the distribution function of X is (Figure 3.1.1)Figure 3.1.1 The distribution function in Example 3.1.3 3. PropertiesThe distribution function ()F x of a random variable X has the following properties:SolutionBy definition,1(2000)(2000)10.6321P X F e -≤==-=.Question ： What are the probabilities (2000)P X < and (2000)P X =?SolutionLet 1X be the total number shown, then the events 1{}X k = contains 1k - sample points, 2,3,4,5k =. Thus11()36k P X k -==, 2,3,4,5k = AndsoThus Figure 3.1.2 The distribution function in Example 3.1.53.2 Discrete Random Variables 离散型随机变量In this book, we study two kinds of random variables. ,,}n aAssume a discrete random variable X takes values from the set 12{,,,}n X a a a =. Let()n n P X a p ==,1,2,.n = (3.2.1) Then we have 0n p ≥, 1,2,,n = 1n n p=∑.the probability distribution of the discrete random variable X (概率分布)注意随机变量X 的分布所满足的条件(1) P i ≥0(2) P 1+P 2+…+P n =1离散型分布函数 And the distribution function of X is given by()()n n a xF x P X x p ≤=≤=∑ (3.2.2)Solutionn=3, p=1/2X p r01/813/823/831/8two-point distribution(两点分布)某学生参加考试得5分的概率是p, X表示他首次得5分的考试次数，求X的分布。
计量经济学中英文词汇对照
Controlled experiments Conventional depth Convolution Corrected factor Corrected mean Correction coefficient Correctness Correlation coefficient Correlation index Correspondence Counting Counts Covaห้องสมุดไป่ตู้iance Covariant Cox Regression Criteria for fitting Criteria of least squares Critical ratio Critical region Critical value
Asymmetric distribution Asymptotic bias Asymptotic efficiency Asymptotic variance Attributable risk Attribute data Attribution Autocorrelation Autocorrelation of residuals Average Average confidence interval length Average growth rate BBB Bar chart Bar graph Base period Bayes' theorem Bell-shaped curve Bernoulli distribution Best-trim estimator Bias Binary logistic regression Binomial distribution Bisquare Bivariate Correlate Bivariate normal distribution Bivariate normal population Biweight interval Biweight M-estimator Block BMDP(Biomedical computer programs) Boxplots Breakdown bound CCC Canonical correlation Caption Case-control study Categorical variable Catenary Cauchy distribution Cause-and-effect relationship Cell Censoring
Bidirectional reflectance distribution function
Bidirectional reflectance distributionfunction Diagram showing vectors used to define the BRDF.All vectors areunit length.ωi points toward the light source.ωr points towardthe viewer(camera).n is the surface normal.The bidirectional reflectance distribution function(BRDF;f r(ωi,ωr))is a function of four real variablesthat defines how light is reflected at an opaque surface.It is employed both in the optics of real-world light,incomputer graphics algorithms,and in computer vision al-gorithms.The function takes an incoming light direction,ωi,and outgoing direction,ωr(taken in a coordinate sys-tem where the surface normal n lies along the z-axis),andreturns the ratio of reflected radiance exiting alongωr tothe irradiance incident on the surface from directionωi.Each directionωis itself parameterized by azimuth angleϕand zenith angleθ,therefore the BRDF as a whole isa function of4variables.The BRDF has units sr−1,withsteradians(sr)being a unit of solid angle.1DefinitionThe BRDF wasfirst defined by Fred Nicodemus around1965.[1]The definition is:f r(ωi,ωr)=d L r(ωr)d E i(ωi)=d L r(ωr)L i(ωi)cosθi dωiwhere L is radiance,or power per unit solid-angle-in-the-direction-of-a-ray per unit projected-area-perpendicular-to-the-ray,E is irradiance,or power per unit surface area, andθi is the angle betweenωi and the surface normal,n .The index i indicates incident light,whereas the index r indicates reflected light.The reason the function is defined as a quotient of two differentials and not directly as a quotient between the undifferentiated quantities,is because other irradiatinglight than d E i(ωi),which are of no interest for f r(ωi,ωr) ,might illuminate the surface which would unintention-ally affect L r(ωr),whereas d L r(ωr)is only affected by d E i(ωi).2Related functionsThe Spatially Varying Bidirectional Reflectance Dis-tribution Function(SVBRDF)is a6-dimensional func-tion,f r(ωi,ωr,x),where x describes a2D location over an object’s surface.The Bidirectional Texture Function(BTF)is appro-priate for modeling non-flat surfaces,and has the same parameterization as the SVBRDF;however in contrast, the BTF includes non-local scattering effects like shad-owing,masking,interreflections or subsurface scattering. The functions defined by the BTF at each point on the surface are thus called Apparent BRDFs.The Bidirectional Surface Scattering Reflectance Dis-tribution Function(BSSRDF),is a further generalized 8-dimensional function S(x i,ωi,x r,ωr)in which light entering the surface may scatter internally and exit at an-other location.In all these cases,the dependence on the wavelength of light has been ignored and binned into RGB channels. In reality,the BRDF is wavelength dependent,and to account for effects such as iridescence or luminescence the dependence on wavelength must be made explicit: f r(λi,ωi,λr,ωr).3Physically based BRDFsPhysically realistic BRDFs have additional properties,[2] including,•positivity:f r(ωi,ωr)≥0•obeying Helmholtz reciprocity:f r(ωi,ωr)=f r(ωr,ωi)•conserving energy:∀ωr,∫Ωf r(ωi,ωr)cosθi dωi≤1127SEE ALSO4ApplicationsThe BRDF is a fundamental radiometric concept,and ac-cordingly is used in computer graphics for photorealistic rendering of synthetic scenes(see the rendering equa-tion),as well as in computer vision for many inverse prob-lems such as object recognition.BRDF has also been used for modeling light trapping in solar cells(ing the OPTOS formalism)or low concentration solar photo-voltaic systems.[3][4]In the context of satellite remote sensing,NASA uses a BRDF model to characterise surface anisotropy.For a given land area,the BRDF is established based on se-lected multiangular observations of surface reflectance. While single observations depend on view geometry and solar angle,the MODIS BRDF/Albedo product describes intrinsic surface properties in several spectral bands,at a resolution of500meters.[5]The BRDF/Albedo product can be used to model surface albedo depending on atmo-spheric scattering.5ModelsBRDFs can be measured directly from real objects using calibrated cameras and lightsources;[6]however,many phenomenological and analytic models have been pro-posed including the Lambertian reflectance model fre-quently assumed in computer graphics.Some useful fea-tures of recent models include:•accommodating anisotropic reflection •editable using a small number of intuitive parame-ters•accounting for Fresnel effects at grazing angles •being well-suited to Monte Carlo methods.W.Matusik et al.found that interpolating between mea-sured samples produced realistic results and was easy to understand.[7]5.1Some examples•Lambertian model,representing perfectly diffuse (matte)surfaces by a constant BRDF.•Lommel–Seeliger,lunar and Martian reflection.•Phong reflectance model,a phenomenological model akin to plastic-like specularity.[8]•Blinn–Phong model,resembling Phong,but allow-ing for certain quantities to be interpolated,reducing computational overhead.[9]•Torrance–Sparrow model,a general model repre-senting surfaces as distributions of perfectly spec-ular microfacets.[10]•Cook–Torrance model,a specular-microfacet model(Torrance–Sparrow)accounting for wave-length and thus color shifting.[11]•Ward model,a specular-microfacet model with an elliptical-Gaussian distribution function dependent on surface tangent orientation(in addition to surface normal).[12]•Oren–Nayar model,a“directed-diffuse”microfacet model,with perfectly diffuse(rather than specular) microfacets.[13]•Ashikhmin-Shirley model,allowing for anisotropic reflectance,along with a diffuse substrate under a specular surface.[14]•HTSG(He,Torrance,Sillion,Greenberg),a compre-hensive physically based model.[15]•Fitted Lafortune model,a generalization of Phong with multiple specular lobes,and intended for para-metricfits of measured data.[16]•Lebedev model for analytical-grid BRDF approximation.[17]6AcquisitionTraditionally,BRDF measurements were taken for one specific lighting and viewing direction at a time using gonioreflectometers.Unfortunately,using such a device to densely measure the BRDF is very time consuming. One of thefirst improvements on these techniques used a half-silvered mirror and a digital camera to take many BRDF samples of a planar target at once.Since this work, many researchers have developed other devices for effi-ciently acquiring BRDFs from real world samples,and it remains an active area of research.There is an alternative way to measure BRDF based on HDR images.The standard algorithm is to measure the BRDF point cloud from images and optimize it by one of the BRDF models.[18]7See also•Albedo•BSDF•Gonioreflectometer•Opposition spike•Photometry(astronomy)3•Radiometry•Reflectance•Schlick’s approximation•Specular highlight8References[1]Nicodemus,Fred(1965).“Directional reflectance andemissivity of an opaque surface”(abstract).Applied Op-tics.4(7):767–775.Bibcode:1965ApOpt...4..767N.doi:10.1364/AO.4.000767.[2]Duvenhage,Bernardt(2013).“Numerical verification ofbidirectional reflectance distribution functions for physi-cal plausibility”.Proceedings of the South African Insti-tute for Computer Scientists and Information Technologists Conference.pp.200–208.[3]Andrews,Rob W.;Pollard,Andrew;Pearce,JoshuaM.,"Photovoltaic system performance enhancement with non-tracking planar concentrators:Experimental results and BRDF based modelling,”Photovoltaic Specialists Conference(PVSC),2013IEEE39th,pp.0229,0234,16–21June2013.doi:10.1109/PVSC.2013.6744136 [4]Andrews,R.W.;Pollard,A.;Pearce,J.M.,“PhotovoltaicSystem Performance Enhancement With Nontracking Planar Concentrators:Experimental Results and Bidirec-tional Reflectance Function(BDRF)-Based Modeling,”IEEE Journal of Photovoltaics5(6),pp.1626-1635(2015).DOI:10.1109/JPHOTOV.2015.2478064[5]“BRDF/Albedo”.NASA,Goddard Space Flight Center.Retrieved March9,2017.[6]Rusinkiewicz,S.“A Survey of BRDF Representation forComputer Graphics”.Retrieved2007-09-05.[7]Wojciech Matusik,Hanspeter Pfister,Matt Brand,andLeonard McMillan.A Data-Driven Reflectance Model.ACM Transactions on Graphics.22(3)2002.[8] B.T.Phong,Illumination for computer generated pic-tures,Communications of ACM18(1975),no.6,311–317.[9]James F.Blinn(1977).“Models of light reflection forcomputer synthesized pictures”.Proc.4th annual con-ference on computer graphics and interactive techniques: 192.doi:10.1145/563858.563893.[10]K.Torrance and E.Sparrow.Theory for Off-Specular Re-flection from Roughened Surfaces.J.Optical Soc.Amer-ica,vol.57.1967.pp.1105–1114.[11]R.Cook and K.Torrance.“A reflectance model for com-puter graphics”.Computer Graphics(SIGGRAPH'81 Proceedings),Vol.15,No.3,July1981,pp.301–316.[12]Ward,Gregory J.(1992).“Measuring and modelinganisotropic reflection”.Proceedings of SIGGRAPH.pp.265–272.doi:10.1145/133994.134078.[13]S.K.Nayar and M.Oren,"Generalization of the Lamber-tian Model and Implications for Machine Vision".Inter-national Journal on Computer Vision,Vol.14,No.3,pp.227–251,Apr,1995[14]Michael Ashikhmin,Peter Shirley,An Anisotropic PhongBRDF Model,Journal of Graphics Tools2000[15]X.He,K.Torrance,F.Sillon,and D.Greenberg,A com-prehensive physical model for light reflection,Computer Graphics25(1991),no.Annual Conference Series,175–186.[16] fortune,S.Foo,K.Torrance,and D.Greenberg,Non-linear approximation of reflectance functions.In Turner Whitted,editor,SIGGRAPH97Conference Pro-ceedings,Annual Conference Series,pp.117–126.ACM SIGGRAPH,Addison Wesley,August1997.[17]Ilyin A.,Lebedev A.,Sinyavsky V.,Ignatenko,A.,Image-based modelling of material reflective properties offlat objects(In Russian).In:GraphiCon'2009.;2009.p.198-201.[18]BRDFRecon project9Further reading•Lubin,Dan;Robert Massom(2006-02-10).Polar Remote Sensing.Volume I:Atmosphere and Oceans (1st ed.).Springer.p.756.ISBN3-540-43097-0.•Matt,Pharr;Greg Humphreys(2004).Physically Based Rendering(1st ed.).Morgan Kauffmann.p.1019.ISBN0-12-553180-X.•Schaepman-Strub,G.;M.E.Schaepman;T.H.Painter;S.Dangel;J.V.Martonchik(2006-07-15).“Reflectance quantities in optical re-mote sensing:definitions and case studies”.Re-mote Sensing of Environment.103(1):27–42.doi:10.1016/j.rse.2006.03.002.Retrieved2015-11-01.•An intuitive introduction to the concept of reflection model and BRDF.410TEXT AND IMAGE SOURCES,CONTRIBUTORS,AND LICENSES 10Text and image sources,contributors,and licenses10.1Text•Bidirectional reflectance distribution function Source:https:///wiki/Bidirectional_reflectance_distribution_function?oldid=778971918Contributors:Meekohi,Charles Matthews,Ldo,Altenmann,DocWatson42,Richie,Rich Farmbrough,Hooperbloob, Waldir,Srleffler,Kri,Jaraalbe,Dhwoow,Banus,Deuar,SmackBot,KYN,Chris the speller,Pietaster,Drewnoakes,Tsca.bot,Ieth wk, Jurohi,Dicklyon,Plewis,Barticus88,Escarbot,Magioladitis,Cdecoro,Pruthvi.Vallabh,Antarktis~enwiki,Selinger,Blueclaw,Dhatfield, Svick,Rilak,Jakarr,Swindbot,Addbot,DOI bot,Zacao,Legobot,Luckas-bot,Yobot,AnomieBOT,Rubinbot,Citation bot,Martin Kraus, Pmlineditor,Ivan Shmakov,Tom.Reding,Lanser1989,Jnnewn,Git2010,Helpful Pixie Bot,Bibcode Bot,Eheitz,BG19bot,YFdyh-bot,So-ravux,Mark viking,Ekips39,Tentinator,Stack Overflow,Naeschdy,Monkbot,Gondi56,AkhilKallepalli1290,Buntuhug,Fmadd,Blaesi, L8ManeValidus,Petra Sieber(SLU)and Anonymous:4510.2Images•File:5-cell.gif Source:https:///wikipedia/commons/d/d8/5-cell.gif License:Public domain Contributors:Transferred from en.wikipedia to Commons.Original artist:JasonHise at English Wikipedia•File:BRDF_Diagram.svg Source:https:///wikipedia/commons/e/ed/BRDF_Diagram.svg License:CC BY-SA3.0 Contributors:•BRDF_Diagram.png Original artist:BRDF_Diagram.png:Meekohi10.3Content license•Creative Commons Attribution-Share Alike3.0。
概率论分布函数
概率论分布函数概率论分布函数是概率论中的重要概念，它描述了一个随机变量取不同值的概率。
通过分布函数，我们可以了解随机变量的分布情况，从而进行概率计算和数据分析。
本文将介绍概率论分布函数的定义、性质以及常见的分布函数类型。
一、定义概率论分布函数，也称累积分布函数（Cumulative Distribution Function，简称CDF），是描述一个随机变量取不同值的概率的函数，通常用F(x)表示。
对于任意实数x，F(x)定义为：F(x) = P(X≤x)其中，X表示随机变量。
概率论分布函数的定义可以从两个角度理解：1.几何角度：概率论分布函数描述了随机变量取值小于等于某个x 的概率，即在数轴上，小于等于x的区间的长度与整个概率空间的比例。
2.概率角度：概率论分布函数定义了对于任意取值小于等于x的情况下，随机变量取该值的概率。
二、性质概率论分布函数具有以下性质：1.非减性：对于任意的x1<x2，有F(x1)≤F(x2)。
这是因为随机变量在小于等于x1的区间上取值的概率一定小于等于小于等于x2的区间上取值的概率。
2.有界性：对于任意的x，有0≤F(x)≤1。
概率的范围是从0到1，因此概率论分布函数的取值也在这个范围内。
3.右连续性：对于任意的x0，有lim(x→x0+)F(x)=F(x0)。
这表示当x无限接近x0时，概率论分布函数的值会无限接近于F(x0)。
4.左极限性：对于任意的x0，有lim(x→x0-)F(x)=F(x0-1)。
这表示当x无限接近x0时，概率论分布函数的值会无限接近于F(x0-1)。
以上性质是概率论分布函数的基本特征，它们保证了分布函数的合理性和准确性。
三、常见的分布函数类型在概率论中，常见的分布函数类型有很多，下面介绍其中几个常见的分布函数：1.均匀分布函数（Uniform Distribution Function）：均匀分布函数是最简单的分布函数之一，它表示随机变量的取值在一个区间上均匀分布。
统计学基础专业词汇
population---总体sampling unit---抽样单元sample---样本observed value---观测值descriptive statistics---描述性统计量random sample---随机样本simple random sample---简单随机样本statistics---统计量order statistic---次序统计量sample range---样本极差mid-range---中程数estimator---估计量sample median---样本中位数sample moment of order k---k阶样本矩sample mean---样本均值average---平均数arithmetic mean---算数平均值sample variance---样本方差sample standard deviation---样本标准差sample coefficient of variation---样本变异系数standardized sample random variable---标准化样本随机变量sample skewness coefficient---样本偏度系数sample kurtosis coefficient---样本峰度系数sample covariance---样本协方差sample correlation coefficient---样本相关系数standard error---标准误差interval estimator---区间估计statistical tolerance interval---统计容忍区间statistical tolerance limit---统计容忍限confidence interval---置信区间one-sided confidence interval---单侧置信区间prediction interval---预测区间estimate---估计值error of estimation---估计误差bias---偏差unbiased estimator---无偏估计量maximum likelihood estimator---极大似然估计量estimation---估计maximum likelihood estimation---极大似然估计likelihood function---似然函数profile likelihood function---剖面函数hypothesis---假设null hypothesis---原假设alternative hypothesis---备择假设simple hypothesis---简单假设composite hypothesis---复合假设significance level---显著性水平type i error---第一类错误type ii error---第二类错误statistical test---统计检验significance test---显著性检验p-value---p值power of a test---检验功效power curve---功效曲线test statistic---检验统计量graphical descriptive statistics---图形描述性统计量numerical descriptive statistics---数值描述性统计量classes---类(组)class---类(组)class limits; class boundaries---组限mid-point of class---组中值class width---组距frequency---频数frequency distribution---频数分布histogram---直方图bar chart---条形图cumulative frequency---累积频数relative frequency---频率cumulative relative frequency---累积频率sample space---样本空间event---事件complementary event---对立事件independent events---独立事件probability [of an event A]---[事件A的]概率conditional probability---条件概率distribution function [of a random variable x]---[随机变量X的]分布函数family of distributions---分布族parameter---参数random variable---随机变量probability distribution---概率分布distribution---分布expectation---期望p-quantile---p分位数median---中位数quartile---四分位数one-dimensional probability distribution---一维概率分布one-dimensional distribution---一维分布multivariate probability distribution---多维概率分布multivariate distribution---多维分布marginal probability distribution---边缘概率分布marginal distribution---边缘分布conditional probability distribution---条件概率分布conditional distribution---条件分布regression curve---回归曲线regression surface---回归曲面discrete probability distribution---离散概率分布discrete distribution---离散分布continuous probability distribution---连续概率分布continuous distribution---连续分布probability [mass] function---概率函数mode of probability [mass] function---概率函数的众数probability density function---概率密度函数mode of probability density function---概率密度函数的众数discrete random variable---离散随机变量continuous random variable---连续随机变量centred probability distribution---中心化概率分布centred random variable---中心化随机变量standardized probability distribution---标准化概率分布standardized random variable---标准化随机变量moment of order r---r阶[原点]矩means---均值moment of order r = 1---一阶矩mean---均值variance---方差standard deviation---标准差coefficient of variation---变异系数coefficient of skewness---偏度系数coefficient of kurtosis---峰度系数joint moment of order r and s---(r,s)阶联合[原点]矩joint central moment of order r and s---(r,s)阶联合中心矩covariance---协方差correlation coefficient---相关系数multinomial distribution---多项分布binomial distribution---二项分布poisson distribution---泊松分布hypergeometric distribution---超几何分布negative binomial distribution---负二项分布normal distribution, gaussian distribution---正态分布standard normal distribution, standard gaussian distribution---标准正态分布lognormal distribution---对数正态分布t distribution, student's distribution---t分布degrees of freedom---自由度f distribution---f分布gamma distribution---伽玛分布，t分布chi-squared distribution---卡方分布，x²分布exponential distribution---指数分布beta distribution---贝塔分布，β分布uniform distribution, rectangular distribution---均匀分布type i value distribution, gumbel distribution---i型极值分布type ii value distribution, gumbel distribution---ii型极值分布weibull distribution---韦布尔分布type iii value distribution, gumbel distribution---iii型极值分布multivariate normal distribution---多维正态分布bivariate normal distribution---二维正态分布standard bivariate normal distribution---标准二维正态分布sampling distribution---抽样分布probability space---概率空间analysis of variance (anova)---方差分析covariance---协方差correlation coefficient---相关系数linear regression---线性回归multiple regression---多元回归logistic regression---逻辑回归principal component analysis (pca)---主成分分析cluster analysis---聚类分析factor analysis---因子分析bayesian statistics---贝叶斯统计time series analysis---时间序列分析non-parametric statistics---非参数统计survival analysis---生存分析data mining---数据挖掘machine learning---机器学习big data---大数据decision tree---决策树random forest---随机森林support vector machine (svm)---支持向量机neural network---神经网络deep learning---深度学习outlier detection---异常值检测cross validation---交叉验证moment---矩conditional probability---条件概率joint distribution---联合分布marginal distribution---边缘分布bayes' theorem---贝叶斯定理central limit theorem---中心极限定理law of large numbers---大数定律likelihood function---似然函数consistent estimator---一致性估计point estimation---点估计interval estimation---区间估计decision theory---决策理论bayesian estimation---贝叶斯估计sequential analysis---序列分析stochastic process---随机过程markov chain---马尔可夫链poisson process---泊松过程random sampling---随机抽样stratified sampling---分层抽样systematic sampling---系统抽样cluster sampling---簇抽样nonparametric test---非参数检验chi-square test---卡方检验t-test---t 检验f-test---f 检验。
matlab卡方分布函数
matlab卡方分布函数一、什么是卡方分布卡方分布（Chi-Square Distribution）是一种常见的概率分布，它在统计学中有着重要的应用。
卡方分布通常用于检验两个或多个样本是否来自于同一个总体，以及判断某些事件是否独立发生。
二、卡方分布函数的定义卡方分布函数（Chi-Square Distribution Function）是指随机变量 X 服从自由度为 k 的卡方分布时，其概率密度函数为：f(x) = 1/(2^(k/2)*Gamma(k/2)) * x^(k/2-1) * e^(-x/2)其中 Gamma 表示欧拉伽马函数，x ≥ 0。
三、matlab中的卡方分布函数在 matlab 中，可以使用 chi2pdf 函数计算卡方分布的概率密度函数值。
该函数的语法格式为：y = chi2pdf(x, k)其中 x 表示自变量（即随机变量 X 的取值），k 表示自由度。
y 表示因变量（即概率密度函数值）。
四、matlab中的例子下面给出一个例子来说明如何使用 matlab 中的 chi2pdf 函数。
假设有一组数据如下：data = [4, 3, 5, 6, 7, 8, 9]我们想要检验这组数据是否符合正态分布。
为了进行检验，我们需要计算样本数据的卡方值。
首先，我们需要计算样本数据的均值和标准差：mean_value = mean(data)std_value = std(data)然后，我们需要根据均值和标准差生成一组正态分布的随机数：norm_data = normrnd(mean_value, std_value, 1, length(data))接下来，我们使用 chi2pdf 函数计算样本数据的卡方值：chi2_value = sum((data - norm_data).^2 ./ norm_data)最后，我们可以使用chi2inv 函数计算自由度为n 的卡方分布上限值：upper_limit = chi2inv(0.95, length(data)-1)如果样本数据的卡方值小于自由度为 n 的卡方分布上限值，则认为这组数据符合正态分布；否则认为不符合。
我校的奖品分配活动 Prize Distribution Function 英语作文
Prize Distribution Function InMy SchoolPrize distribution function is important for encouraging the efficient working of a school. It comes only once a year. This generates new enthusiasm in the students. A strong link is established between the parents of the students and the school staff. This function holds great significance in the school diary.This year the prize distribution function attracted a large audience consisting of parents and invitees. This prize-giving function of the school was held on the fifteenth of January. The director of education was invited to grace the occasion as the chief guest. The preparations for the function started a month earlier. The school building was whitewashed. The schoolhall where the function was to be held, was beautifully decorated with pictures and charts.On the appointed day, a beautiful table and some chairs were placed on the stage. The carpets were spread to accommodate the children and in the remaining part of the hall, chairs were arranged. The front rows were reserved for teachers and invitees. The function was supposed to start at 4 p.m. By 3.45 p.m. the hall was jam-packed with visitors who were very impressed with the arrangements made by the students. In one corner, there was a table where the prizes and trophies had been arranged. Now, all of us were eagerly waiting for the arrival of the chief guest.At the appointed time, the director of education arrived. He was accorded a warm welcome bythe principal and the senior members of the school staff. As he entered the hall, the school band played in his honour. All the students and the audience stood up as a mark of respect. The director of education was garlanded by the principal and by some senior members of the staff. As soon as the chief guest occupied his seat, there was pin-drop silence in the hall.The principal began by giving a brief introduction and a life-sketch of the chief guest. Later, she read the annual report of the school, giving an account of the past achievements of the school. At the same time, she requested the chief guest to enhance the annual grant that was quite insufficient in view of the students’ interest in manifold activities.The principal instructed the president of the Literary Club to begin with the cultural programme. Some students sang melodious songs. “Prince and the Wood Cutter” of Six One Act Plays was staged next. The participants got thunderous applause from the audience for their wonderful talent that they displayed in acting and presentation. The students who took part in this play, seemed to be well- prepared. Folk-dances added a colourful touch to the show.The chief guest who presided over the function gave away the prizes to the winners. I got a trophy for getting first rank in my class and certificate for my runner-up position in drawing competition. I felt elated as my parents and my little sister encouraged and praised me. The director delivered a short speech wherein he praised the performance of the students andencouraged them to participate still more enthusiastically. He also admired the sense of discipline imbibed by the students during the entire function. Then the principal got up and thanked the director for his kind visit to the school.Finally, the function came to an end with everyone singing the National Anthem. The following day was declared a holiday by the principal.。
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distribution function
分布函数是研究随机变量的一般性质及其可能取值的函数，它是特定随机变量的可能取值的概率分布的函数。
它是随机变量的概率模型的重要工具，它的定义是：分布函数F(x)是指具有概率密度函数f(x)的一系列随机变量X的一维函数，它是随机变量X取值所有可能结果的总和。
分布函数在数学上可以被定义为：设X为一个随机变量，其可能取值为 x_1, x_2, x_3...x_n则X的分布函数F(x)为：
F(x) = P(X≤x) = P(x_1≤x) + P(x_2≤x) + P(x_3≤x) + ... + P(x_n≤x)
在概率论中，分布函数用于描述单个随机变量的总体分布，它必须满足一些特定的条件，例如：
1.于任意x，0≤F(x)≤1；
2.x趋近于非变体时，F(x)收敛于0；
3.x趋近于正无穷时，F(x)收敛于1；
4.于任意两个不相等的x_1和x_2，F(x_1)≤F(x_2).
此外，分布函数（CDF）也可以用来描述多个随机变量间的关系，从而可以用来确定概率，这可以用来建立概率图，从而更好地推断概率论概率和概率关系。
分布函数有多种类型，这些类型可以用来描述各种各样的随机变量，例如：正态分布函数、卡方分布函数、伽马分布函数、贝塔分布函数等。
各种分布函数的形式和特性都不同，在应用时，我们一般会
选择合适的分布函数来描述随机变量的概率分布。
最后，分布函数在金融领域中也有重要的应用，用于衡量数据分析、价格定价以及风险估计等，例如：利率曲线模型旨在根据历史数据来分析及预测未来利率变动，而其中，分布函数占据了重要的作用。
总之，分布函数是随机变量概率模型的一个重要工具，它的作用及应用无处不在，它的正确使用可以有助于我们更好、更有效地分析概率图，从而有效地解决实际问题。