Vijay K. Rohatgi, A. K. Md. Ehsanes Saleh

An Introduction to Probability and Statistics (eBook, ePUB)

• Format: ePub

Produktbeschreibung

A well-balanced introduction to probability theory and mathematical statistics Featuring updated material, An Introduction to Probability and Statistics, Third Edition remains a solid overview to probability theory and mathematical statistics. Divided intothree parts, the Third Edition begins by presenting the fundamentals and foundationsof probability. The second part addresses statistical inference, and the remainingchapters focus on special topics. An Introduction to Probability and Statistics, Third Edition includes: * A new section on regression analysis to include multiple regression, logistic regression, and Poisson regression * A reorganized chapter on large sample theory to emphasize the growing role of asymptotic statistics * Additional topical coverage on bootstrapping, estimation procedures, and resampling * Discussions on invariance, ancillary statistics, conjugate prior distributions, and invariant confidence intervals * Over 550 problems and answers to most problems, as well as 350 worked out examples and 200 remarks * Numerous figures to further illustrate examples and proofs throughout An Introduction to Probability and Statistics, Third Edition is an ideal reference and resource for scientists and engineers in the fields of statistics, mathematics, physics, industrial management, and engineering. The book is also an excellent text for upper-undergraduate and graduate-level students majoring in probability and statistics.

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Produktdetails

• Verlag: John Wiley & Sons
• Seitenzahl: 728
• Erscheinungstermin: 2. September 2015
• Englisch
• ISBN-13: 9781118799659
• Artikelnr.: 43825474

Autorenporträt

Vijay K. Rohatgi, PhD, is Professor Emeritus in the Department of Mathematics and Statistics at Bowling Green State University. An Investment Research Consultant for PRI Investments, he is also the author of several books and over 100 research papers. A. K. Md. Ehsanes Saleh, PhD, is Distinguished Research Professor in the School of Mathematics and Statistics at Carleton University. Dr. Saleh is the author of more than 200 journal articles, and his research interests include nonparametric statistics, order statistics, and robust estimation.

Inhaltsangabe

PREFACE TO THE THIRD EDITION xiii PREFACE TO THE SECOND EDITION xv PREFACE
TO THE FIRST EDITION xvii ACKNOWLEDGMENTS xix ENUMERATION OF THEOREMS AND
REFERENCES xxi 1 Probability 1 1.1 Introduction 1 1.2 Sample Space 2 1.3
Probability Axioms 7 1.4 Combinatorics: Probability on Finite Sample Spaces
20 1.5 Conditional Probability and Bayes Theorem 26 1.6 Independence of
Events 31 2 Random Variables and Their Probability Distributions 39 2.1
Introduction 39 2.2 Random Variables 39 2.3 Probability Distribution of a
Random Variable 42 2.4 Discrete and Continuous Random Variables 47 2.5
Functions of a Random Variable 55 3 Moments and Generating Functions 67 3.1
Introduction 67 3.2 Moments of a Distribution Function 67 3.3 Generating
Functions 83 3.4 Some Moment Inequalities 93 4 Multiple Random Variables 99
4.1 Introduction 99 4.2 Multiple Random Variables 99 4.3 Independent Random
Variables 114 4.4 Functions of Several Random Variables 123 4.5 Covariance,
Correlation and Moments 143 4.6 Conditional Expectation 157 4.7 Order
Statistics and Their Distributions 164 5 Some Special Distributions 173 5.1
Introduction 173 5.2 Some Discrete Distributions 173 5.2.1 Degenerate
Distribution 173 5.2.2 Two-Point Distribution 174 5.2.3 Uniform
Distribution on n Points 175 5.2.4 Binomial Distribution 176 5.2.5 Negative
Binomial Distribution (Pascal or Waiting Time Distribution) 178 5.2.6
Hypergeometric Distribution 183 5.2.7 Negative Hypergeometric Distribution
185 5.2.8 Poisson Distribution 186 5.2.9 Multinomial Distribution 189
5.2.10 Multivariate Hypergeometric Distribution 192 5.2.11 Multivariate
Negative Binomial Distribution 192 5.3 Some Continuous Distributions 196
5.3.1 Uniform Distribution (Rectangular Distribution) 199 5.3.2 Gamma
Distribution 202 5.3.3 Beta Distribution 210 5.3.4 Cauchy Distribution 213
5.3.5 Normal Distribution (the Gaussian Law) 216 5.3.6 Some Other
Continuous Distributions 222 5.4 Bivariate and Multivariate Normal
Distributions 228 5.5 Exponential Family of Distributions 240 6 Sample
Statistics and Their Distributions 245 6.1 Introduction 245 6.2 Random
Sampling 246 6.3 Sample Characteristics and Their Distributions 249 6.4
Chi-Square, t-, and F-Distributions: Exact Sampling Distributions 262 6.5
Distribution of (X,S2) in Sampling from a Normal Population 271 6.6
Sampling from a Bivariate Normal Distribution 276 7 Basic Asymptotics:
Large Sample Theory 285 7.1 Introduction 285 7.2 Modes of Convergence 285
7.3 Weak Law of Large Numbers 302 7.4 Strong Law of Large Numbers 308 7.5
Limiting Moment Generating Functions 316 7.6 Central Limit Theorem 321 7.7
Large Sample Theory 331 8 Parametric Point Estimation 337 8.1 Introduction
337 8.2 Problem of Point Estimation 338 8.3 Sufficiency, Completeness and
Ancillarity 342 8.4 Unbiased Estimation 359 8.5 Unbiased Estimation
(Continued): A Lower Bound for the Variance of An Estimator 372 8.6
Substitution Principle (Method of Moments) 386 8.7 Maximum Likelihood
Estimators 388 8.8 Bayes and Minimax Estimation 401 8.9 Principle of
Equivariance 418 9 Neyman-Pearson Theory of Testing of Hypotheses 429 9.1
Introduction 429 9.2 Some Fundamental Notions of Hypotheses Testing 429 9.3
Neyman-Pearson Lemma 438 9.4 Families with Monotone Likelihood Ratio 446
9.5 Unbiased and Invariant Tests 453 9.6 Locally Most Powerful Tests 459 10
Some Further Results on Hypotheses Testing 463 10.1 Introduction 463 10.2
Generalized Likelihood Ratio Tests 463 10.3 Chi-Square Tests 472 10.4
t-Tests 484 10.5 F-Tests 489 10.6 Bayes and Minimax Procedures 491 11
Confidence Estimation 499 11.1 Introduction 499 11.2 Some Fundamental
Notions of Confidence Estimation 499 11.3 Methods of Finding Confidence
Intervals 504 11.4 Shortest-Length Confidence Intervals 517 11.5 Unbiased
and Equivariant Confidence Intervals 523 11.6 Resampling: Bootstrap Method
530 12 General Linear Hypothesis 535 12.1 Introduction 535 12.2 General
Linear Hypothesis 535 12.3 Regression Analysis 543 12.3.1 Multiple Linear
Regression 543 12.3.2 Logistic and Poisson Regression 551 12.4 One-Way
Analysis of Variance 554 12.5 Two-Way Analysis of Variance with One
Observation Per Cell 560 12.6 Two-Way Analysis of Variance with Interaction
566 13 Nonparametric Statistical Inference 575 13.1 Introduction 575 13.2
U-Statistics 576 13.3 Some Single-Sample Problems 584 13.3.1
Goodness-of-Fit Problem 584 13.3.2 Problem of Location 590 13.4 Some
Two-Sample Problems 599 13.4.1 Median Test 601 13.4.2 Kolmogorov-Smirnov
Test 602 13.4.3 The Mann-Whitney-Wilcoxon Test 604 13.5 Tests of
Independence 608 13.5.1 Chi-square Test of Independence--Contingency Tables
608 13.5.2 Kendall's Tau 611 13.5.3 Spearman's Rank Correlation Coefficient
614 13.6 Some Applications of Order Statistics 619 13.7 Robustness 625
13.7.1 Effect of Deviations from Model Assumptions on Some Parametric
Procedures 625 13.7.2 Some Robust Procedures 631 FREQUENTLY USED SYMBOLS
AND ABBREVIATIONS 637 REFERENCES 641 STATISTICAL TABLES 647 ANSWERS TO
SELECTED PROBLEMS 667 AUTHOR INDEX 677 SUBJECT INDEX 679