A Brief Course in Mathematical Statistics

by Tanis, Elliot A.; Hogg, Robert V.

• ISBN13: 9780131751392
• ISBN10: 0131751395
• Edition: 1st
• Format: Paperback
• Copyright: 2006-12-30
• Publisher: Pearson

Summary

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. 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. A comprehensive reference for individuals who need to brush up on their knowledge of statistics.

Author Biography

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

Probability

Basic Concepts

Methods of Enumeration

Conditional Probability

Independent Events

Bayes's Theorem Chapter One Comments

Discrete Distributions

Discrete Probability Distributions

Expectations

Special Discrete Distributions

Estimation

Linear Functions of Independent Random Variables

Multivariate Discrete Distributions Chapter Two Comments

Continuous Distributions

Descriptive Statistics and EDA

Continuous Probability Distributions

Special Continuous Distributions

The Normal Distribution

Estimation in the Continuous Case

The Central Limit Theorem

Approximations for Discrete Distributions Chapter Three Comemnts

Applications of Statistical Inference

Summary of Necessary Theoretical Results

Confidence Intervals Using X2 F,and T

Confidence Intervals and Tests of Hypotheses

Basic Tests Concerning One Parameter

Tests of the Equality of Two Parameters

Simple Linear Regression

More on Linear Regression

One-Factor Analysis of Variance

Distribution-Free Confidence and Tolerance Intervals

Chi-Square Goodness of Fit Tests

Contingency Tables Chapter Four Comments

Computer Oriented Techniques

Computation of Statistics

Computer Algebra Systems

Simulation

Resampling Chapter Five Comments

Some Sampling Distribution Theory

Moment-Generation Function Technique

M.G.F of Linear Functions

Limiting Moment-Generating Functions

Use of Order Statistics in Non-regular Cases Chapter Six Comments

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