
Probability and Statistical Inference
by Bartoszynski, Robert; Niewiadomska-Bugaj, Magdalena-
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Summary
Author Biography
The late Robert Bartoszynski, PhD, was Professor in the Department of Statistics at The Ohio State University. His scientific contributions included research in the theory of stochastic processes and modeling biological phenomena. Throughout his career, Dr. Bartoszynski published over 80 journal articles, books, and book chapters. He was a Fellow of the Institute of Mathematical Statistics as well as a member of the American Statistical Association, the International Statistical Institute, and the Bernoulli Society.
Magdalena Niewiadomska-Bugaj, PhD, is Professor in the Department of Statistics at Western Michigan University. An active member of numerous societies including the American Statistical Association, the Institute of Mathematical Statistics, and the Classification Society of North America, Dr. Niewiadomska-Bugaj's areas of interest include general statistical methodology, nonparametric statistics, classification, and categorical data analysis. She has published over 50 papers, books, and book chapters in theoretical and applied statistics.
Table of Contents
Preface | p. x |
Experiments, Sample Spaces, and Events | p. 1 |
Introduction | p. 1 |
Sample Space | p. 2 |
Algebra of Events | p. 9 |
Infinite Operations on Events | p. 16 |
Probability | p. 25 |
Introduction | p. 25 |
Probability as a Frequency | p. 25 |
Axioms of Probability | p. 26 |
Consequences of the Axioms | p. 31 |
Classical Probability | p. 36 |
Necessity of the Axioms | p. 37 |
Subjective Probability | p. 42 |
Counting | p. 47 |
Introduction | p. 47 |
Product Sets, Orderings, and Permutations | p. 47 |
Binomial Coefficients | p. 55 |
Extension of Newton's Formula | p. 68 |
Multinomial Coefficients | p. 69 |
Conditional Probability: Independence | p. 73 |
Introduction | p. 73 |
Conditional Probability | p. 74 |
Partitions; Total Probability Formula | p. 80 |
Bayes' Formula | p. 87 |
Independence | p. 92 |
Exchangeability; Conditional Independence | p. 99 |
Markov Chains* | p. 103 |
Introduction and Basic Definitions | p. 103 |
Definition of a Markov Chain | p. 106 |
n-Step Transition Probabilities | p. 111 |
The Ergodic Theorem | p. 114 |
Absorption Probabilities | p. 122 |
Random Variables: Univariate Case | p. 125 |
Introduction | p. 125 |
Distributions of Random Variables | p. 126 |
Discrete and Continuous Random Variables | p. 139 |
Functions of Random Variables | p. 150 |
Survival and Hazard Functions | p. 157 |
Random Variables: Multivariate Case | p. 161 |
Bivariate Distributions | p. 161 |
Marginal Distributions; Independence | p. 168 |
Conditional Distributions | p. 180 |
Bivariate Transformations | p. 187 |
Multidimensional Distributions | p. 196 |
Expectation | p. 203 |
Introduction | p. 203 |
Expected Value | p. 204 |
Expectation as an Integral* | p. 212 |
Properties of Expectation | p. 220 |
Moments | p. 228 |
Variance | p. 236 |
Conditional Expectation | p. 248 |
Inequalities | p. 252 |
Selected Families of Distributions | p. 257 |
Bernoulli Trials and Related Distributions | p. 257 |
Hypergeometric Distribution | p. 270 |
Poisson Distribution and Poisson Process | p. 276 |
Exponential, Gamma and Related Distributions | p. 290 |
Normal Distribution | p. 296 |
Beta Distribution | p. 306 |
Random Samples | p. 311 |
Statistics and their Distributions | p. 311 |
Distributions Related to Normal | p. 313 |
Order Statistics | p. 319 |
Generating Random Samples | p. 325 |
Convergence | p. 330 |
Central Limit Theorem | p. 342 |
Introduction to Statistical Inference | p. 351 |
Overview | p. 351 |
Descriptive Statistics | p. 353 |
Basic Model | p. 358 |
Bayesian Statistics | p. 360 |
Sampling | p. 360 |
Measurement Scales | p. 367 |
Estimation | p. 373 |
Introduction | p. 373 |
Consistency | p. 378 |
Loss, Risk, and Admissibility | p. 381 |
Efficiency | p. 386 |
Methods of Obtaining Estimators | p. 394 |
Sufficiency | p. 424 |
Interval Estimation | p. 440 |
Testing Statistical Hypotheses | p. 455 |
Introduction | p. 455 |
Intuitive Background | p. 460 |
Most Powerful Tests | p. 469 |
Uniformly Most Powerful Tests | p. 481 |
Unbiased Tests | p. 487 |
Generalized Likelihood Ratio Tests | p. 491 |
Conditional Tests | p. 498 |
Tests and Confidence Intervals | p. 501 |
Review of Tests for Normal Distributions | p. 502 |
Monte Carlo, Bootstrap, and Permutation Tests | p. 512 |
Linear Models | p. 517 |
Introduction | p. 517 |
Regression of the First and Second Kind | p. 519 |
Distributional Assumptions | p. 525 |
Linear Regression in the Normal Case | p. 528 |
Testing Linearity | p. 535 |
Prediction | p. 538 |
Inverse Regression | p. 540 |
BLUE | p. 542 |
Regression Toward the Mean | p. 545 |
Analysis of Variance | p. 546 |
One-Way Layout | p. 547 |
Two-Way Layout | p. 550 |
ANOVA Models with Interaction | p. 553 |
Further Extensions | p. 557 |
Rank Methods | p. 559 |
Introduction | p. 559 |
Glivenko-Cantelli Theorem | p. 560 |
Kolmogorov-Smirnov Tests | p. 564 |
One-Sample Rank Tests | p. 571 |
Two-Sample Rank Tests | p. 578 |
Kruskal-Wallis Test | p. 582 |
Analysis of Categorical Data | p. 585 |
Introduction | p. 585 |
Chi-Square Tests | p. 587 |
Homogeneity and Independence | p. 593 |
Consistency and Power | p. 599 |
2 x 2 Contingency Tables | p. 604 |
r x c Contingency Tables | p. 612 |
Statistical Tables | p. 617 |
Bibliography | p. 629 |
Answers to Odd-Numbered Problems | p. 634 |
Index | p. 642 |
Table of Contents provided by Ingram. All Rights Reserved. |
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