Samaniego F.J. Stochastic Modeling and Mathematical Statistics: A Text for Statisticians and Quantitative Scientists

CRC Press, 2014. — 622 p.A Bit of Background
Approaches to Modeling Randomness
The Axioms of Probability
Conditional Probability
Bayes' Theorem
Independence
Counting
Chapter Problems
Random Variables
Mathematical Expectation
The Hypergeometric Model
A Brief Tutorial on Mathematical Induction (Optional)
The Binomial Model
The Geometric and Negative Binomial Models
The Poisson Model
MomentGenerating Functions
Chapter Problems
Continuous Random Variables
Mathematical Expectation for Continuous Random Variables
Cumulative Distribution Functions
The Gamma Model
The Normal Model
Other Continuous Models
The Beta Model
The Double Exponential Distribution
The Lognormal Model
The Pareto Distribution
The Weibull Distribution
The Cauchy Distribution
Contents note continued: The Logistic Model
Chapter Problems
Bivariate Distributions
More on Mathematical Expectation
Independence
The Multinomial Distribution (Optional)
The Multivariate Normal Distribution
Transformation Theory
The Method of MomentGenerating Functions
The Method of Distribution Functions
The ChangeofVariable Technique
Order Statistics
Chapter Problems
Chebyshev's Inequality and Its Applications
Convergence of Distribution Functions
The Central Limit Theorem
The Delta Method Theorem
Chapter Problems
Basic Principles
Further Insights into Unbiasedness
Fisher Information, the CramerRao Inequality, and Best Unbiased Estimators
Sufficiency, Completeness, and Related Ideas
Optimality within the Class of Linear Unbiased Estimators
Beyond Unbiasedness
Chapter Problems
Contents note continued: Basic Principles
The Method of Moments
Maximum Likelihood Estimation
A Featured Example: Maximum Likelihood Estimation of the Risk of Disease Based on Data from a Prospective Study of Disease
The NewtonRaphson Algorithm
A Featured Example: Maximum Likelihood Estimation from Incomplete Data via the EM Algorithm
Chapter Problems
Exact Confidence Intervals
Approximate Confidence Intervals
Sample Size Calculations
Tolerance Intervals (Optional)
Chapter Problems
The Bayesian Paradigm
Deriving Bayes Estimators
Exploring the Relative Performance of Bayes and Frequentist Estimators
A Theoretical Framework for Comparing Bayes vs Frequentist Estimators
Bayesian Interval Estimation
Chapter Problems
0Basic Principles
0Standard Tests for Means and Proportions
0Sample Size Requirements for Achieving Prespecified Power
0Optimal Tests: The NeymanPearson Lemma
0Likelihood Ratio Tests
0Testing the Goodness of Fit of a Probability Model
0Fatherly Advice about the Perils of Hypothesis Testing (Optional)
0Chapter Problems
Simple Linear Regression
Some Distribution Theory for Simple Linear Regression
Theoretical Properties of Estimators and Tests under the SLR Model
OneWay Analysis of Variance
The Likelihood Ratio Test in OneWay ANOVA
Chapter Problems
Nonparametric Estimation
The Nonparametric Bootstrap
The Sign Test
The Runs Test
The Rank Sum Test
Chapter Problems