Application statistical method

Content Introduction

Application Statistical Methods is based on the graduate teaching experience accumulated by edits for many years, and is prepared with reference to the basic requirements of the Ministry of Education's "Master's Application Statistics Courses". As a technological, economic, management, agronomics, doctoral degree, doctoral student and senior undergraduate student learning statistical analysis method (or application mathematical statistics) courses, can also be used as relevant disciplines and engineering technicians Reference book.

Book catalog

Chapter 1 Probability Theory Basic Basic

§1.1 Random Event and Its Probability

One, Sample Space and Random Event

II, the probability of the event

three, conditional probability and multiplication formula

four, the independence of the event

§1.2 random variable And its distribution

1. Random variables and distribution functions

two, multi-dimensional random variables and distributions thereof

3, random variable function distribution

§1.3 Random variables

1. Mathematical expectations

two, variance

three, random variable "Standardization" and moment

4, mathematical expectations and variance of common distribution and variance

5, covariance and correlation coefficient

6, multi-dimensional random variable digital characteristics

1.4 Extremely limited preliminary

1. Convergence of random variable sequence

two, large law

three, central extreme limit

Exercise 1 / P>

Chapter 2 Mathematical Basic Concepts and Sampling Distribution

2.1 Mathematical Statistics Basic Concept

1, Overall and Samples

2, statistics

2.2 Experience distribution function and histogram

1. Experience distribution function

two, histogram

< P> §2.3 Common Probability Distribution

1, X2 Distribution

2, T Distribution

3, F Distribution

four, Position point of probability distribution

§2.4 Sampling Distribution

1, the normal sample distribution

2, some sampling distribution of non-state / p>

exercises 2

Chapter IV parameter estimate

3.1 estimate

1, mission method

two , Greatly likelihood estimation method

three, Bayes estimation

§3.2 Evaluation criteria

1, non-bore

II, effectiveness

three, consistency

§3.3 estimation

§3.4 Regional overall parameters estimate

< P> First, the overall situation

two, the overall situation

3.5 Assembly of non-normal parameters Estimate

1, index distribution parameters Interval estimated

2, 0-1 Interval estimation of parameters

3.6 single-side confidence interval

exercises three

Four chapters hypothesis test

4.1 Assumption test Basic concept

1. Problem proposing

II, assumptioning the basic principle

Third, assume the two categories of test Error

4, hypotheses the general step of the test

4.2 hypothetical inspection of a single normal overall parameter

1. Assumption test of a single normal overall mean < / p>

two, the hypothetical assay of single normal variance

4.3 hypothetical test of two normal overall parameters

1, two normal overall mean Assumption test

two, the hypothetical assay of two normal variance

4.4 Assumption test of the non-state overall parameter

1, index distribution parameters Assumption test

two, 0-1 distribution parameters hypothesis test

exercise four

Chapter 5 regression analysis

5.1 Analysis

1. Simple correlation coefficient

2, the inspection of the correlation coefficient

5.2 Linear regression model


II, the basic concept of regression analysis

three, linear regression model

5.3 minimum multiplier estimate and its nature

one , Least squares estimate

two, one-unit linear regression

three, minimum multiplier estimation properties

5.4 regression equation and regression coefficient test


2, the F Test of the Regression Equation

Third, the Significant Inspection of Regression Coefficients

5.5 Due to Variables Prediction

1. Point prediction

two, interval prediction

§5.6 self-variable selection and gradual return

one, self Criteria

2, select the optimal regression equation

three, gradually return

§5.7 nonlinear regression

one, Larid nonlinear model

two, general nonlinear regression model

exercise five

Chapter 6 Non-parameter statistics preliminary

< P> 6.1 Non-parametric hypothesis test

1, distribution function combination verification

2, the independent test of the listing table

three, consistency Inspection

4 Parameter regression model

exercise six

Seventh chapter variance analysis and orthogonal test design

7.1 single factor variance analysis

one , Single factor test


1. Double-factor analysis of interaction

2, no interaction of biplomerative variance analysis

7.3 is trying Design

1, 正 交 交表

2, orthogonal test without interaction

three, interacting orthogonal test

Exercise Seven / P>

Chapter 8 Multivatical Analysis

8.1 Multi-Wide Radio Variable

1. Multi-Wide Radio Variable

Two , Multi-normal distribution

three, sampling and statistics

four, parameter estimation

8.2 discriminant analysis and cluster analysis

1. Distance

2 The principle of analysis

2, the sample main component calculation step

exercise eight

Appendix I common distribution parameters, estimated quantity and digital features - Overview P>

Appendix II Common distribution table

Schedule 1 Poisson distribution table

Schedule 2 Standard normal distribution table

Schedule 3t distribution Upper point table

Schedule 4X2 distribution upper point table

Schedule 5F distribution upper point table

Schedule 6 Related Coefficient Test Table

Schedule 7 Symbol Table

Schedule 8 Symbol Rank and Table

Appendix III 正 交

exercise answer

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