APS 专业审核考试 Quantitive analysis 定性分析

Quantitative analysis
决策法Decision making
1)确定型问题：可以提出确定结果的方案
2)风险型型问题：存在两种以上的自然状态，可以估算概率，都会承担一定的风险
3)不确定型问题：存在两种以上的自然状态，无法估算概率
定量分析quantitative analysis
1.定量分析模型的表示方法
1)Form method
2)Matrix method
3)Decision tree method
2.定量分析的基本分析方法
1)确定型问题：一个状态多种方案→直接比较法
例子：存钱。

不同年份不同interest rate
2)不确定型问题：Matrix method 例子：夏天进空调
等概率准侧a=b；
决策系数准则o< a,b< 1；
Max max乐观准则a=1 b=0；
Conservative Criterion：Min准则a=0 b=1
最大后悔值最小regret
3)风险型问题：知道几种状态，和概率Decision tree method +期望值
Types of data:
1) Categorical data. 例子：Female-male, Arts-Science, weight-black
2) Ordinal data:exist on an ordinal scale, but no real zero
例子：bachelor-master-doctor
3) Numeric data: zero, can be calculated
Data distribution: 中间值middle value
Centralized tendency: 和上面的数据分类一一对应
1) Mode:the most common value among a group
2) Median:The median of a finite list of numbers can be found by arranging all the
observations from lowest value to highest value and picking the middle one
例子Me=(n+1)/2 {3, 3, 5, 9, 11} is 5 {3, 5, 7, 9} is (5 + 7) / 2 = 6
Quartile：Q L=(n+1)/4 Q H=3(n+1)/4
3) Mean：Numeral number
Tendency of dispersion（dispersive）:
1) variation ratio：f m = the frequency (number of cases) of the mode
2) Quartile deviation：Q D= Q H– Q L
3) xmax-xmin
Square deviation：σ2
Standard Deviation：σ
Quantitative analysis
置信区间：Confidence interval ; fiducial 1 interval is a measure of the reliability of an estimate.
样本均值关键值 × 样本均值的标准误差；即
如果不知道总体方差σ，那么用样本方差s 代替σ
Hypothesis testing
1. Null 2 hypothesis ：H 0
Alternative hypothesis ：H 1
αerror is serious than ß error
so we control the
α
error, and give a certain probability. Usually, α is very small, 0.05
3. The testing process
1. state the relevant null and alternative hypotheses.
2. Need a sample
3. Select a significance level (α). Common values are 5% and 1%.
4. test statistic, compare with Z 1-α or Z α or Z 1-α/2
大样本z ，小样本t 总体σ已知，用σ，σ未知，用样本方差s 单词表： μ
0 假设的总体均值 test statistic 检验统计量
critical region 拒绝域
1
adj. [测] 基准的；信托的；根据信仰的 2 adj. 无效的，无价值的；等于零的
n
X z σμ0-=
检验统计量.xls
Quantitative analysis 2
Regression analysis-- estimating the relationships among variables
Regression analysis helps one understand how the value of the dependent variable (or 'criterion variable') changes when any one of the independent variables is varied, while the other independent variables are held fixed.
No exact relationship between dependent and independent variable.
We use a large number of historical data and mathematical statistics method try to find a rule and to prognoses the dependent variable.
Unary linear regression equation: Y= a+ bx learning hours and note
Time series analysis method
Time series forecasting is the use of a model to predict future values based on previously observed values.
Cannot find influence factors and no need to find out the causal relationship。