A Brief Course in Mathematical Statistics / Edition 1

by Elliot Tanis, Robert Hogg

Overview

This innovative new introduction to Mathematical Statistics covers the important concept of estimation at a point much earlier (Chapter 2) than others on this subject. KEY TOPICS: Applies mathematical statistics to topics such as insurance, Pap smear tests, estimating the number of whales in an ocean, fitting models, filling 12 ounce containers, environmental issues, and results in certain sporting events. Includes summaries of the most important aspects of discrete distributions, continuous distributions, confidence intervals, and tests of hypotheses. Provides computer applications for data analysis and also for theoretical solutions such as simulation and bootstrapping. MARKET: A comprehensive reference for individuals who need to brush up on their knowledge of statistics.

Product Details

ISBN-13:	9780131751392
Publisher:	Pearson Education
Publication date:	12/30/2006
Edition description:	New Edition
Pages:	368
Product dimensions:	8.00(w) x 10.00(h) x 0.70(d)

About the Author

Elliot A. Tanis: Tanis has written 30 articles in probability and statistics, many illustrating applications using the computer. He has authored or co-authored four books in probability and statistics. These include “Probability & Statistics Explorations with MAPLE,” 2^nd edition, with Zaven Karian in 1999 and “Probability and Statistical Inference,” 7^th edition, with Robert V. Hogg in 2006. He was Chairperson (1976-77) and Governor (1989-92) of the Michigan Section of the Mathematical Association of America. He was a winner of the Hope’s Outstanding Professor Educator (H.O.P.E.) award in 1989 and received the award for Distinguished College or University Teaching of Mathematics, Michigan Section, MAA, in 1992. Tanis became Professor Emeritus of Mathematics at Hope College in 2000 after teaching there 35 years.

Robert V. Hogg: Hogg has written over 70 research articles and coauthored five books, including “Introduction of Mathematical Statistics,” 6^th edition, with J. W. McKean and A.T. Craig, and “Probability and Statistical Inference,” 7^th edition, with E.A. Tanis. He was President of the American Statistical Association in 1988 and was given the Founders and Noether awards of that society. Earlier he received an Outstanding Teacher award of the Mathematical Association of America and, in 2007, will receive the Carver Medal from the Institute of Mathematical Statistics. Hogg became Professor Emeritus of Statistics at the University of Iowa in 2001 after teaching there 51 years.

Table of Contents

Preface

1. Probability

1.1 Basic Concepts

1.2 Methods of Enumeration

1.3 Conditional Probability

1.4 Independent Events

1.5 Bayes's Theorem

Chapter One Comments

2. Discrete Distributions

2.1 Discrete Probability Distributions

2.2 Expectations

2.3 Special Discrete Distributions

2.4 Estimation

2.5 Linear Functions of Independent Random Variables

2.6 Multivariate Discrete Distributions

Chapter Two Comments

3. Continuous Distributions

3.1 Descriptive Statistics and EDA

3.2 Continuous Probability Distributions

3.3 Special Continuous Distributions

3.4 The Normal Distribution

3.5 Estimation in the Continuous Case

3.6 The Central Limit Theorem

3.7 Approximations for Discrete Distributions

Chapter Three Comemnts

4. Applications of Statistical Inference

4.1 Summary of Necessary Theoretical Results

4.2 Confidence Intervals Using _X² F,and T

4.3 Confidence Intervals and Tests of Hypotheses

4.4 Basic Tests Concerning One Parameter

4.5 Tests of the Equality of Two Parameters

4.6 Simple Linear Regression

4.7 More on Linear Regression

4.8 One-Factor Analysis of Variance

4.9 Distribution-Free Confidence and Tolerance Intervals

4.10 Chi-Square Goodness of Fit Tests

4.11 Contingency Tables

Chapter Four Comments

5. Computer Oriented Techniques

5.1 Computation of Statistics

5.2 Computer Algebra Systems

5.3 Simulation

5.4 Resampling

Chapter Five Comments

6. Some Sampling Distribution Theory

6.1 Moment-Generation Function Technique

6.2 M.G.F of Linear Functions

6.3 Limiting Moment-Generating Functions

6.4 Use of Order Statistics in Non-regular Cases

Chapter Six Comments

Editorial Reviews

"The authors have years of experience analyzing real data, have collected excellent examples to illustrate statistical concepts and anomalies, and are proven writers in the discipline." Professor Charles Sommer, SUNY College at Brockport

"The authors have done a wonderful job in writing this book...I must congratulate them for doing a great job and helping in the development of the subject of Statistics." Professor M.L. Aggarwal, The University of Memphis

From the Publisher