Stochastic Modeling and Mathematical Statistics: A Text for Statisticians and Quantitative Scientists

Content: Machine generated contents note: 1.1.A Bit of Background --
1.2.Approaches to Modeling Randomness --
1.3.The Axioms of Probability --
1.4.Conditional Probability --
1.5.Bayes' Theorem --
1.6.Independence --
1.7.Counting --
1.8.Chapter Problems --
2.1.Random Variables --
2.2.Mathematical Expectation --
2.3.The Hypergeometric Model --
2.4.A Brief Tutorial on Mathematical Induction (Optional) --
2.5.The Binomial Model --
2.6.The Geometric and Negative Binomial Models --
2.7.The Poisson Model --
2.8.Moment-Generating Functions --
2.9.Chapter Problems --
3.1.Continuous Random Variables --
3.2.Mathematical Expectation for Continuous Random Variables --
3.3.Cumulative Distribution Functions --
3.4.The Gamma Model --
3.5.The Normal Model --
3.6.Other Continuous Models --
3.6.1.The Beta Model --
3.6.2.The Double Exponential Distribution --
3.6.3.The Lognormal Model --
3.6.4.The Pareto Distribution --
3.6.5.The Weibull Distribution --
3.6.6.The Cauchy Distribution --
Contents note continued: 3.6.7.The Logistic Model --
3.7.Chapter Problems --
4.1.Bivariate Distributions --
4.2.More on Mathematical Expectation --
4.3.Independence --
4.4.The Multinomial Distribution (Optional) --
4.5.The Multivariate Normal Distribution --
4.6.Transformation Theory --
4.6.1.The Method of Moment-Generating Functions --
4.6.2.The Method of Distribution Functions --
4.6.3.The Change-of-Variable Technique --
4.7.Order Statistics --
4.8.Chapter Problems --
5.1.Chebyshev's Inequality and Its Applications --
5.2.Convergence of Distribution Functions --
5.3.The Central Limit Theorem --
5.4.The Delta Method Theorem --
5.5.Chapter Problems --
6.1.Basic Principles --
6.2.Further Insights into Unbiasedness --
6.3.Fisher Information, the Cramer-Rao Inequality, and Best Unbiased Estimators --
6.4.Sufficiency, Completeness, and Related Ideas --
6.5.Optimality within the Class of Linear Unbiased Estimators --
6.6.Beyond Unbiasedness --
6.7.Chapter Problems --
Contents note continued: 7.1.Basic Principles --
7.2.The Method of Moments --
7.3.Maximum Likelihood Estimation --
7.4.A Featured Example: Maximum Likelihood Estimation of the Risk of Disease Based on Data from a Prospective Study of Disease --
7.5.The Newton-Raphson Algorithm --
7.6.A Featured Example: Maximum Likelihood Estimation from Incomplete Data via the EM Algorithm --
7.7.Chapter Problems --
8.1.Exact Confidence Intervals --
8.2.Approximate Confidence Intervals --
8.3.Sample Size Calculations --
8.4.Tolerance Intervals (Optional) --
8.5.Chapter Problems --
9.1.The Bayesian Paradigm --
9.2.Deriving Bayes Estimators --
9.3.Exploring the Relative Performance of Bayes and Frequentist Estimators --
9.4.A Theoretical Framework for Comparing Bayes vs. Frequentist Estimators --
9.5.Bayesian Interval Estimation --
9.6.Chapter Problems --
10.1.Basic Principles --
10.2.Standard Tests for Means and Proportions --
10.3.Sample Size Requirements for Achieving Pre-specified Power --
Contents note continued: 10.4.Optimal Tests: The Neyman-Pearson Lemma --
10.5.Likelihood Ratio Tests --
10.6.Testing the Goodness of Fit of a Probability Model --
10.7.Fatherly Advice about the Perils of Hypothesis Testing (Optional) --
10.8.Chapter Problems --
11.1.Simple Linear Regression --
11.2.Some Distribution Theory for Simple Linear Regression --
11.3.Theoretical Properties of Estimators and Tests under the SLR Model --
11.4.One-Way Analysis of Variance --
11.5.The Likelihood Ratio Test in One-Way ANOVA --
11.6.Chapter Problems --
12.1.Nonparametric Estimation --
12.2.The Nonparametric Bootstrap --
12.3.The Sign Test --
12.4.The Runs Test --
12.5.The Rank Sum Test --
12.6.Chapter Problems