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Contents

1 Introduction
1.1 Background
1.2 Data sets
1.3 References

2 Summarizing Data
2.1 Tabular and graphical procedures
2.2 Numerical summary measures

3 Probability
3.1 Algebra of sets
3.2 Combinatorial methods
3.3 Probability
3.4 Random variables
3.5 Mathematical expectation
3.6 Multivariate distributions
3.7 Inequalities

4 Functions of Random Variables
4.1 Finding the probability distribution
4.2 Sums of random variables
4.3 Sampling distributions
4.4 Finite population
4.5 Theorems
4.6 Order statistics
4.7 Range and studentized range

5 Discrete Probability Distributions
5.1 Bernoulli distribution
5.2 Beta binomial distribution
5.3 Beta Pascal distribution
5.4 Binomial distribution
5.5 Geometric distribution
5.6 Hypergeometric distribution
5.7 Multinomial distribution
5.8 Negative binomial distribution
5.9 Poisson distribution
5.10 Rectangular (discrete uniform) distribution

6 Continuous Probability Distributions
6.1 Arcsin distribution
6.2 Beta distribution
6.3 Cauchy distribution
6.4 Chi–square distribution
6.5 Erlang distribution
6.6 Exponential distribution
6.7 Extreme–value distribution
6.8 F distribution
6.9 Gamma distribution
6.10 Half–normal distribution
6.11 Inverse Gaussian (Wald) distribution
6.12 Laplace distribution
6.13 Logistic distribution
6.14 Lognormal distribution
6.15 Noncentral chi–square distribution
6.16 Noncentral F distribution
6.17 Noncentral t distribution
6.18 Normal distribution
6.19 Normal distribution: multivariate
6.20 Pareto distribution
6.21 Power function distribution
6.22 Rayleigh distribution
6.23 t distribution
6.24 Triangular distribution
6.25 Uniformdistributio n
6.26 Weibull distribution
6.27 Relationships among distributions

7 Standard Normal Distribution
7.1 Density function and related functions
7.2 Critical values
7.3 Tolerance factors for normal distributions
7.4 Operating characteristic curves
7.5 Multivariate normal distribution
7.6 Distribution of the correlation coefficient
7.7 Circular normal probabilities
7.8 Circular error probabilities

8 Estimation
8.1 Definitions
8.2 Cram′er–Rao inequality
8.3 Theorems
8.4 The method of moments
8.5 The likelihood function
8.6 The method of maximum likelihood
8.7 Invariance property of MLEs
8.8 Different estimators
8.9 Estimators for small samples
8.10 Estimators for large samples

9 Confidence Intervals
9.1 Definitions
9.2 Common critical values
9.3 Sample size calculations
9.4 Summary of common confidence intervals
9.5 Confidence intervals: one sample
9.6 Confidence intervals: two samples
9.7 Finite population correction factor

10 Hypothesis Testing
10.1 Introduction
10.2 The Neyman–Pearson lemma
10.3 Likelihood ratio tests
10.4 Goodness of fit test
10.5 Contingency tables
10.6 Bartlett’s test
10.7 Cochran’s test
10.8 Number of observations required
10.9 Critical values for testing outliers
10.10 Significance test in 2×2 contingency tables
10.11 Determining values in Bernoulli trials

11 Regression Analysis
11.1 Simple linear regression
11.2 Multiple linear regression
11.3 Orthogonal polynomials

12 Analysis of Variance
12.1 One-way anova
12.2 Two-way anova
12.3 Three-factor experiments
12.4 Manova
12.5 Factor analysis
12.6 Latin square design

13 Experimental Design
13.1 Latin squares
13.2 Graeco–Latin squares
13.3 Block designs
13.4 Factorial experimentation: 2 factors
13.5 2r Factorial experiments
13.6 Confounding in 2n factorial experiments
13.7 Tables for design of experiments
13.8 References

14 Nonparametric Statistics
14.1 Friedman test for randomized block design
14.2 Kendall’s rank correlation coefficient
14.3 Kolmogorov–Smirnoff tests
14.4 Kruskal–Wallis test
14.5 The runs test
14.6 The sign test
14.7 Spearman’s rank correlation coefficient
14.8 Wilcoxon matched-pairs signed-ranks test
14.9 Wilcoxon rank–sum(Mann–Whitney ) test
14.10 Wilcoxon signed-rank test

15 Quality Control and Risk Analysis
15.1 Quality assurance
15.2 Acceptance sampling
15.3 Reliability
15.4 Risk analysis and decision rules

16 General Linear Models
16.1 Notation
16.2 The general linear model
16.3 Summary of rules for matrix operations
16.4 Quadratic forms
16.5 General linear hypothesis of full rank
16.6 General linear model of less than full rank

17 Miscellaneous Topics
17.1 Geometric probability
17.2 Information and communication theory
17.3 Kalman filtering
17.4 Large deviations (theory of rare events)
17.5 Markov chains
17.6 Martingales
17.7 Measure theoretical probability
17.8 Monte Carlo integration techniques
17.9 Queuing theory
17.10 Random matrix eigenvalues
17.11 Random number generation
17.12 Resampling methods
17.13 Self-similar processes
17.14 Signal processing
17.15 Stochastic calculus
17.16 Classic and interesting problems
17.17 Electronic resources
17.18 Tables

18 Special Functions
18.1 Bessel functions
18.2 Beta function
18.3 Ceiling and floor functions
18.4 Delta function
18.5 Error functions
18.6 Exponential function
18.7 Factorials and Pochhammer’s symbol
18.8 Gamma function
18.9 Hypergeometric functions
18.10 Logarithmic functions
18.11 Partitions
18.12 Signumfunctio n
18.13 Stirling numbers
18.14 Sums of powers of integers
18.15 Tables of orthogonal polynomials
18.16 References

Notation