An introduction to probability and statistics / V. K. Rohatgi, A. K. Md. Ehsanes Saleh.

Format:

Book

Author/Creator:

Rohatgi, V. K., 1939- author.

Saleh, A. K. Md. Ehsanes, author.

Series:

Wiley series in probability and statistics.

Wiley Series in Probability and Statistics

Language:

English

Subjects (All):

Probabilities.

Mathematical statistics.

Physical Description:

1 online resource (xviii, 689 pages) : illustrations.

Edition:

Third edition.

Place of Publication:

Hoboken, New Jersey : Wiley, 2015.

Summary:

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.

Contents:

Intro

TITLE PAGE

TABLE OF CONTENTS

PREFACE TO THE THIRD EDITION

PREFACE TO THE SECOND EDITION

PREFACE TO THE FIRST EDITION

ACKNOWLEDGMENTS

ENUMERATION OF THEOREMS AND REFERENCES

1 PROBABILITY

1.1 INTRODUCTION

1.2 SAMPLE SPACE

1.3 PROBABILITY AXIOMS

1.4 COMBINATORICS: PROBABILITY ON FINITE SAMPLE SPACES

1.5 CONDITIONAL PROBABILITY AND BAYES THEOREM

1.6 INDEPENDENCE OF EVENTS

2 RANDOM VARIABLES AND THEIR PROBABILITY DISTRIBUTIONS

2.1 INTRODUCTION

2.2 RANDOM VARIABLES

2.3 PROBABILITY DISTRIBUTION OF A RANDOM VARIABLE

2.4 DISCRETE AND CONTINUOUS RANDOM VARIABLES

2.5 FUNCTIONS OF A RANDOM VARIABLE

3 MOMENTS AND GENERATING FUNCTIONS

3.1 INTRODUCTION

3.2 MOMENTS OF A DISTRIBUTION FUNCTION

3.3 GENERATING FUNCTIONS

3.4 SOME MOMENT INEQUALITIES

4 MULTIPLE RANDOM VARIABLES

4.1 INTRODUCTION

4.2 MULTIPLE RANDOM VARIABLES

4.3 INDEPENDENT RANDOM VARIABLES

4.4 FUNCTIONS OF SEVERAL RANDOM VARIABLES

4.5 COVARIANCE, CORRELATION AND MOMENTS

4.6 CONDITIONAL EXPECTATION

4.7 ORDER STATISTICS AND THEIR DISTRIBUTIONS

5 SOME SPECIAL DISTRIBUTIONS

5.1 INTRODUCTION

5.2 SOME DISCRETE DISTRIBUTIONS

5.3 SOME CONTINUOUS DISTRIBUTIONS

5.4 BIVARIATE AND MULTIVARIATE NORMAL DISTRIBUTIONS

5.5 EXPONENTIAL FAMILY OF DISTRIBUTIONS

6 SAMPLE STATISTICS AND THEIR DISTRIBUTIONS

6.1 INTRODUCTION

6.2 RANDOM SAMPLING

6.3 SAMPLE CHARACTERISTICS AND THEIR DISTRIBUTIONS

6.4 CHI-SQUARE, t-, AND F-DISTRIBUTIONS: EXACT SAMPLING DISTRIBUTIONS

6.5 DISTRIBUTION OF IN SAMPLING FROM A NORMAL POPULATION

6.6 SAMPLING FROM A BIVARIATE NORMAL DISTRIBUTION

7 BASIC ASYMPTOTICS: LARGE SAMPLE THEORY

7.1 INTRODUCTION

7.2 MODES OF CONVERGENCE

7.3 WEAK LAW OF LARGE NUMBERS

7.4 STRONG LAW OF LARGE NUMBERS†

7.5 LIMITING MOMENT GENERATING FUNCTIONS.

7.6 CENTRAL LIMIT THEOREM

7.7 LARGE SAMPLE THEORY

8 PARAMETRIC POINT ESTIMATION

8.1 INTRODUCTION

8.2 PROBLEM OF POINT ESTIMATION

8.3 SUFFICIENCY, COMPLETENESS AND ANCILLARITY

8.4 UNBIASED ESTIMATION

8.5 UNBIASED ESTIMATION (CONTINUED): A LOWER BOUND FOR THE VARIANCE OF AN ESTIMATOR

8.6 SUBSTITUTION PRINCIPLE (METHOD OF MOMENTS)

8.7 MAXIMUM LIKELIHOOD ESTIMATORS

8.8 BAYES AND MINIMAX ESTIMATION

8.9 PRINCIPLE OF EQUIVARIANCE

9 NEYMAN-PEARSON THEORY OF TESTING OF HYPOTHESES

9.1 INTRODUCTION

9.2 SOME FUNDAMENTAL NOTIONS OF HYPOTHESES TESTING

9.3 NEYMAN-PEARSON LEMMA

9.4 FAMILIES WITH MONOTONE LIKELIHOOD RATIO

9.5 UNBIASED AND INVARIANT TESTS

9.6 LOCALLY MOST POWERFUL TESTS

10 SOME FURTHER RESULTS ON HYPOTHESES TESTING

10.1 INTRODUCTION

10.2 GENERALIZED LIKELIHOOD RATIO TESTS

10.3 CHI-SQUARE TESTS

10.4 t-TESTS

10.5 F-TESTS

10.6 BAYES AND MINIMAX PROCEDURES

11 CONFIDENCE ESTIMATION

11.1 INTRODUCTION

11.2 SOME FUNDAMENTAL NOTIONS OF CONFIDENCE ESTIMATION

11.3 METHODS OF FINDING CONFIDENCE INTERVALS

11.4 SHORTEST-LENGTH CONFIDENCE INTERVALS

11.5 UNBIASED AND EQUIVARIANT CONFIDENCE INTERVALS

11.6 RESAMPLING: BOOTSTRAP METHOD

12 GENERAL LINEAR HYPOTHESIS

12.1 INTRODUCTION

12.2 GENERAL LINEAR HYPOTHESIS

12.3 REGRESSION ANALYSIS

12.4 ONE-WAY ANALYSIS OF VARIANCE

12.5 TWO-WAY ANALYSIS OF VARIANCE WITH ONE OBSERVATION PER CELL

12.6 TWO-WAY ANALYSIS OF VARIANCE WITH INTERACTION

13 NONPARAMETRIC STATISTICAL INFERENCE

13.1 INTRODUCTION

13.2 U-STATISTICS

13.3 SOME SINGLE-SAMPLE PROBLEMS

13.4 SOME TWO-SAMPLE PROBLEMS

13.5 TESTS OF INDEPENDENCE

13.6 SOME APPLICATIONS OF ORDER STATISTICS

13.7 ROBUSTNESS

FREQUENTLY USED SYMBOLS AND ABBREVIATIONS

REFERENCES

STATISTICAL TABLES

ANSWERS TO SELECTED PROBLEMS

AUTHOR INDEX.

SUBJECT INDEX

WILEY SERIES IN PROBABILITY AND STATISTICS

END USER LICENSE AGREEMENT.

Notes:

MSC 60xx ; 62xx

Includes bibliographical references and indexes.

Description based on print version record.

Other Format:

Print version: Rohatgi, Vijay K. An Introduction to Probability and Statistics

ISBN:

9781118799659

1118799658

9781118799635

1118799631

9781118799680

1118799682

OCLC:

902986846