Mathematica laboratories for mathematical statistics : emphasizing simulation and computer intensive methods /

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Bibliographic Details
Author / Creator:	Baglivo, Jenny A. (Jenny Antoinette)
Imprint:	Philadelphia, Pa. : Society for Industrial and Applied Mathematics ; Alexandria, Va. : American Statistical Association, c2005.
Description:	xx, 260 p. : ill. ; 26 cm + 1 CD-ROM (4 3/4 in.).
Language:	English
Series:	ASA-SIAM series on statistics and applied probability
Subject:	Mathematica (Computer file) Mathematica (Computer file) Mathematical statistics -- Computer simulation. Mathematical statistics -- Computer simulation.
Format:	Print Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/5549183

Hidden Bibliographic Details
ISBN:	0898715660 (pbk.)
Notes:	Includes bibliographical references (p. 241-249) and index.

Table of Contents:

Preface
1. Introductory Probability Concepts
1.1. Definitions
1.2. Kolmogorov axioms
1.3. Counting methods
1.3.1. Permutations and combinations
1.3.2. Partitioning sets
1.3.3. Generating functions
1.4. Conditional probability
1.4.1. Law of total probability
1.4.2. Bayes rule
1.5. Independent events
1.5.1. Repeated trials and mutual independence
1.6. Laboratory problems
1.6.1. Laboratory: Introductory concepts
1.6.2. Additional problem notebooks
2. Discrete Probability Distributions
2.1. Definitions
2.1.1. PDF and CDF for discrete distributions
2.2. Univariate distributions
2.2.1. Example: Discrete uniform distribution
2.2.2. Example: Hypergeometric distribution
2.2.3. Distributions related to Bernoulli experiments
2.2.4. Simple random samples
2.2.5. Example: Poisson distribution
2.3. Joint distributions
2.3.1. Bivariate distributions; marginal distributions
2.3.2. Conditional distributions; independence
2.3.3. Example: Bivariate hypergeometric distribution
2.3.4. Example: Trinomial distribution
2.3.5. Survey analysis
2.3.6. Discrete multivariate distributions
2.3.7. Probability generating functions
2.4. Laboratory problems
2.4.1. Laboratory: Discrete models
2.4.2. Additional problem notebooks
3. Continuous Probability Distributions
3.1. Definitions
3.1.1. PDF and CDF for continuous random variables
3.1.2. Quantiles; percentiles
3.2. Univariate distributions
3.2.1. Example: Uniform distribution
3.2.2. Example: Exponential distribution
3.2.3. Euler gamma function
3.2.4. Example: Gamma distribution
3.2.5. Distributions related to Poisson processes
3.2.6. Example: Cauchy distribution
3.2.7. Example: Normal or Gaussian distribution
3.2.8. Example: Laplace distribution
3.2.9. Transforming continuous random variables
3.3. Joint distributions
3.3.1. Bivariate distributions; marginal distributions
3.3.2. Conditional distributions; independence
3.3.3. Example: Bivariate uniform distribution
3.3.4. Example: Bivariate normal distribution
3.3.5. Transforming continuous random variables
3.3.6. Continuous multivariate distributions
3.4. Laboratory problems
3.4.1. Laboratory: Continuous models
3.4.2. Additional problem notebooks
4. Mathematical Expectation
4.1. Definitions and properties
4.1.1. Discrete distributions
4.1.2. Continuous distributions
4.1.3. Properties
4.2. Mean, variance, standard deviation
4.2.1. Properties
4.2.2. Chebyshev inequality
4.2.3. Markov inequality
4.3. Functions of two or more random variables
4.3.1. Properties
4.3.2. Covariance, correlation
4.3.3. Sample summaries
4.3.4. Conditional expectation; regression
4.4. Linear functions of random variables
4.4.1. Independent normal random variables
4.5. Laboratory problems
4.5.1. Laboratory: Mathematical expectation
4.5.2. Additional problem notebooks
5. Limit Theorems
5.1. Definitions
5.2. Law of large numbers
5.2.1. Example: Monte Carlo evaluation of integrals
5.3. Central limit theorem
5.3.1. Continuity correction
5.3.2. Special cases
5.4. Moment generating functions
5.4.1. Method of moment generating functions
5.4.2. Relationship to the central limit theorem
5.5. Laboratory problems
5.5.1. Laboratory: Sums and averages
5.5.2. Additional problem notebooks
6. Transition to Statistics
6.1. Distributions related to the normal distribution
6.1.1. Chi-square distribution
6.1.2. Student t distribution
6.1.3. F ratio distribution
6.2. Random samples from normal distributions
6.2.1. Sample mean, sample variance
6.2.2. Approximate standardization of the sample mean
6.2.3. Ratio of sample variances
6.3. Multinomial experiments
6.3.1. Multinomial distribution
6.3.2. Goodness-of-fit: Known model
6.3.3. Goodness-of-fit: Estimated model
6.4. Laboratory problems
6.4.1. Laboratory: Transition to statistics
6.4.2. Additional problem notebooks
7. Estimation Theory
7.1. Definitions
7.2. Properties of point estimators
7.2.1. Bias; unbiased estimator
7.2.2. Efficiency for unbiased estimators
7.2.3. Mean squared error
7.2.4. Consistency
7.3. Interval estimation
7.3.1. Example: Normal distribution
7.3.2. Approximate intervals for means
7.4. Method of moments estimation
7.4.1. Single parameter estimation
7.4.2. Multiple parameter estimation
7.5. Maximum likelihood estimation
7.5.1. Single parameter estimation
7.5.2. Cramer-Rao lower bound
7.5.3. Approximate sampling distribution
7.5.4. Multiple parameter estimation
7.6. Laboratory problems
7.6.1. Laboratory: Estimation theory
7.6.2. Additional problem notebooks
8. Hypothesis Testing Theory
8.1. Definitions
8.1.1. Neyman-Pearson framework
8.1.2. Equivalent tests
8.2. Properties of tests
8.2.1. Errors, size, significance level
8.2.2. Power, power function
8.3. Example: Normal distribution
8.3.1. Tests of [mu] = [mu subscript 0]
8.3.2. Tests of [sigma superscript 2] = [sigma superscript 2 subscript o]
8.4. Example: Bernoulli/binomial distribution
8.5. Example: Poisson distribution
8.6. Approximate tests of [mu] = [mu subscript o]
8.7. Likelihood ratio tests
8.7.1. Likelihood ratio statistic; Neyman-Pearson lemma
8.7.2. Generalized likelihood ratio tests
8.7.3. Approximate sampling distribution
8.8. Relationship with confidence intervals
8.9. Laboratory problems
8.9.1. Laboratory: Hypothesis testing
8.9.2. Additional problem notebooks
9. Order Statistics and Quantiles
9.1. Order statistics
9.1.1. Approximate mean and variance
9.2. Confidence intervals for quantiles
9.2.1. Approximate distribution of the sample median
9.2.2. Exact confidence interval procedure
9.3. Sample quantiles
9.3.1. Sample quartiles, sample IQR
9.3.2. Box plots
9.4. Laboratory problems
9.4.1. Laboratory: Order statistics and quantiles
9.4.2. Additional problem notebooks
10. Two Sample Analysis
10.1. Normal distributions: Difference in means
10.1.1. Known variances
10.1.2. Pooled t methods
10.1.3. Welch t methods
10.2. Normal distributions: Ratio of variances
10.3. Large sample: Difference in means
10.4. Rank sum test
10.4.1. Rank sum statistic
10.4.2. Tied observations; midranks
10.4.3. Mann-Whitney U statistic
10.4.4. Shift models
10.5. Sampling models
10.5.1. Population model
10.5.2. Randomization model
10.6. Laboratory problems
10.6.1. Laboratory: Two sample analysis
10.6.2. Additional problem notebooks
11. Permutation Analysis
11.1. Introduction
11.1.1. Permutation tests
11.1.2. Example: Difference in means test
11.1.3. Example: Smirnov two sample test
11.2. Paired sample analysis
11.2.1. Example: Signed rank test
11.2.2. Shift models
11.2.3. Example: Fisher symmetry test
11.3. Correlation analysis
11.3.1. Example: Correlation test
11.3.2. Example: Rank correlation test
11.4. Additional tests and extensions
11.4.1. Example: One sample trend test
11.4.2. Example: Two sample scale test
11.4.3. Stratified analyses
11.5. Laboratory problems
11.5.1. Laboratory: Permutation analysis
11.5.2. Additional problem notebooks
12. Bootstrap Analysis
12.1. Introduction
12.1.1. Approximate conditional estimation
12.2. Bootstrap estimation
12.2.1. Error distribution
12.2.2. Simple approximate confidence interval procedures
12.2.3. Improved intervals: Nonparametric case
12.3. Applications of bootstrap estimation
12.3.1. Single random sample
12.3.2. Independent random samples
12.4. Bootstrap hypothesis testing
12.5. Laboratory problems
12.5.1. Laboratory: Bootstrap analysis
12.5.2. Additional problem notebooks
13. Multiple Sample Analysis
13.1. One-way layout
13.1.1. Example: Analysis of variance
13.1.2. Example: Kruskal-Wallis test
13.1.3. Example: Permutation f test
13.2. Blocked design
13.2.1. Example: Analysis of variance
13.2.2. Example: Friedman test
13.3. Balanced two-way layout
13.3.1. Example: Analysis of variance
13.3.2. Example: Permutation f tests
13.4. Laboratory problems
13.4.1. Laboratory: Multiple sample analysis
13.4.2. Additional problem notebooks
14. Linear Least Squares Analysis
14.1. Simple linear model
14.1.1. Least squares estimation
14.1.2. Permutation confidence interval for slope
14.2. Simple linear regression
14.2.1. Confidence interval procedures
14.2.2. Predicted responses and residuals
14.2.3. Goodness-of-fit
14.3. Multiple linear regression
14.3.1. Least squares estimation
14.3.2. Analysis of variance
14.3.3. Confidence interval procedures
14.3.4. Regression diagnostics
14.4. Bootstrap methods
14.5. Laboratory problems
14.5.1. Laboratory: Linear least squares analysis
14.5.2. Additional problem notebooks
15. Contingency Table Analysis
15.1. Independence analysis
15.1.1. Example: Pearson's chi-square test
15.1.2. Example: Rank correlation test
15.2. Homogeneity analysis
15.2.1. Example: Pearson's chi-square test
15.2.2. Example: Kruskal-Wallis test
15.3. Permutation chi-square tests
15.4. Fourfold tables
15.4.1. Odds ratio analysis
15.4.2. Small sample analyses
15.5. Laboratory problems
15.5.1. Laboratory: Contingency table analysis
15.5.2. Additional problem notebooks
Bibliography
Index

Mathematica laboratories for mathematical statistics : emphasizing simulation and computer intensive methods /

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