Handbook of Statistical Distributions with Applications: 2nd Edition (Hardback) book cover

Handbook of Statistical Distributions with Applications

2nd Edition

By K. Krishnamoorthy

Chapman and Hall/CRC

398 pages | 38 B/W Illus.

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pub: 2015-10-23
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Description

Easy-to-Use Reference and Software for Statistical Modeling and Testing

Handbook of Statistical Distributions with Applications, Second Edition provides quick access to common and specialized probability distributions for modeling practical problems and performing statistical calculations. Along with many new examples and results, this edition includes both the author’s StatCalc software and R codes to accurately and easily carry out computations.

New to the Second Edition

  • Major changes in binomial, Poisson, normal, gamma, Weibull, exponential, logistic, Laplace, and Pareto distributions
  • Updated statistical tests and intervals based on recent publications in statistical journals
  • Enhanced PC calculator StatCalc with electronic help manuals
  • R functions for cases where StatCalc is not applicable, with the codes available online

This highly praised handbook integrates popular probability distribution models, formulas, applications, and software to help you compute a variety of statistical intervals. It covers probability and percentiles, algorithms for random number generation, hypothesis tests, confidence intervals, tolerance intervals, prediction intervals, sample size determination, and much more.

Reviews

Praise for the First Edition:

"… the book has a chance of becoming a highly valued practitioner’s reference …"

"The book is sequentially organized and well structured and many chapters are self-contained. It includes many useful results that are handy for students and practitioners alike….I must say, it is a very useful and handy book for commonly used probability distributions, a one-stop shop! …this is a valuable contribution to [the] scientific community, providing up-to-date coverage on probability distributions and their applications in a systematic fashion. I would like to see this book on my desk! -S.E. Ahmed, Technometrics, July 2016

Journal of the Royal Statistical Society

"I recommend the StatCalc software as a useful quick way to obtain and/or check (relative) simple statistical calculations, and the book as its accompanying manual … many statisticians might find StatCalc a handy addition to their computer desktops, particularly (in my case) with teaching in mind!"

—M.C. Jones, Journal of Applied Statistics, January 2008

"… recommended to statistical practitioners who need a comprehensive yet brief reference on statistical distributions with applications."

—Brian Wiens, The American Statistician, November 2007

"Quite simply, this book is a masterwork. … an essential resource for anyone who models data, or creates applications that require reference to or make use of statistical distribution functions or random variable sampling/generation. The accompanying PC program is a true application in its own right: neat, tidy, and very, very useful. To have this and the book represents a unique reference work. … easily understandable by undergraduate as well as graduate scientists and statisticians … an essential part of the toolkit for professionals working in the quantitative sciences … a remarkable achievement for the author who so obviously has taken great care over many years to assemble and perfect the software and reference work. This is a book worthy of a prize."

—Paul Barrett, University of Auckland, New Zealand

". . . the notes on implementation of distributions will be valuable to users seeking efficient ways to model or find the inverse of a wide range of distributions . . . this is a fairly comprehensive reference guide, well organized and with an authoritative style and many examples."

—Mark Pilling, Royal Statistical Society

Table of Contents

STATCALC

Introduction

Contents of StatCalc

PRELIMINARIES

Random Variables and Expectations

Moments and Other Functions

Some Functions Relevant to Reliability

Model Fitting

Methods of Estimation

Inference

Pivotal-Based Methods for Location-Scale Families

Method of Variance Estimate Recovery

Modified Normal-Based Approximation

Random Number Generation

Some Special Functions

DISCRETE UNIFORM DISTRIBUTION

Description

Moments

BINOMIAL DISTRIBUTION

Description

Moments

Probabilities, Percentiles, and Moments

Proportion

Prediction Intervals

Tolerance Intervals

Tests for the Difference between Two Proportions

Two-Sample Confidence Intervals for Proportions

Confidence Intervals for a Linear Combination of Proportions

Properties and Results

Random Number Generation

Computation of Probabilities

HYPERGEOMETRIC DISTRIBUTION

Description

Moments

Probabilities, Percentiles, and Moments

Point Estimation

Test for the Proportion and Power Calculation

Confidence Interval and Sample Size Calculation

A Test for Comparing Two Proportions

Properties and Results

Random Number Generation

Computation of Probabilities

POISSON DISTRIBUTION

Description

Moments

Probabilities, Percentiles, and Moments

Model Fitting with Examples

One-Sample Inference

Test for the Mean

Confidence Intervals for the Mean

Prediction Intervals

Tolerance Intervals

Tests for Comparing Two Means and Power Calculation

Confidence Intervals for the Ratio of Two Means

Confidence Intervals for the Difference between Two Means

Inference for a Weighted Sum of Poisson Means

Properties and Results

Random Number Generation

Computation of Probabilities

GEOMETRIC DISTRIBUTION

Description

Moments

Probabilities, Percentiles, and Moments

Properties and Results

Random Number Generation

NEGATIVE BINOMIAL DISTRIBUTION

Description

Moments

Probabilities, Percentiles, and Moments

Point Estimation

A Test for the Proportion

Confidence Intervals for the Proportion

Properties and Results

Random Number Generation

A Computational Method for Probabilities

LOGARITHMIC SERIES DISTRIBUTION

Description

Moments

Probabilities, Percentiles, and Moments

Inferences

Properties and Results

Random Number Generation

A Computational Algorithm for Probabilities

CONTINUOUS UNIFORM DISTRIBUTION

Description

Moments

Inferences

Properties and Results

Random Number Generation

NORMAL DISTRIBUTION

Description

Moments

Probabilities, Percentiles, and Moments

One-Sample Inference

Two-Sample Inference

Tolerance Intervals

Properties and Results

Relation to Other Distributions

Random Number Generation

Computing the Distribution Function

CHI-SQUARE DISTRIBUTION

Description

Moments

Probabilities, Percentiles, and Moments

Applications

Properties and Results

Random Number Generation

Computing the Distribution Function

F DISTRIBUTION

Description

Moments

Probabilities, Percentiles, and Moments

Properties and Results

Random Number Generation

A Computational Method for Probabilities

STUDENT'S t DISTRIBUTION

Description

Moments

Probabilities, Percentiles, and Moments

Distribution of the Maximum of Several |t| Variables

Properties and Results

Random Number Generation

Computation of the Distribution Function

EXPONENTIAL DISTRIBUTION

Description

Moments

Probabilities, Percentiles, and Moments

Inferences

Properties and Results

Random Number Generation

GAMMA DISTRIBUTION

Description

Moments

Probabilities, Percentiles, and Moments

Applications with Some Examples

Inferences

Properties and Results

Random Number Generation

A Computational Method for Probabilities

BETA DISTRIBUTION

Description

Moments

Probabilities, Percentiles, and Moments

Inferences

Applications with an Example

Properties and Results

Random Number Generation

Evaluating the Distribution Function

NONCENTRAL CHI-SQUARE DISTRIBUTION

Description

Moments

Probabilities, Percentiles, and Moments

Applications

Properties and Results

Random Number Generation

Evaluating the Distribution Function

NONCENTRAL F DISTRIBUTION

Description

Moments

Computing Table Values

Applications

Properties and Results

Random Number Generation

Evaluating the Distribution Function

NONCENTRAL t DISTRIBUTION

Description

Moments

Probabilities, Percentiles, and Moments

Applications

Properties and Results

Random Number Generation

Evaluating the Distribution Function

LAPLACE DISTRIBUTION

Description

Moments

Probabilities, Percentiles, and Moments

Inferences

Applications

Relation to Other Distributions

Random Number Generation

LOGISTIC DISTRIBUTION

Description

Moments

Probabilities, Percentiles, and Moments

Maximum Likelihood Estimators

Applications

Properties and Results

Random Number Generation

LOGNORMAL DISTRIBUTION

Description

Moments

Probabilities, Percentiles, and Moments

Maximum Likelihood Estimators

Confidence Interval and Test for the Mean

Inferences for the Difference between Two Means

Inferences for the Ratio of Two Means

Applications

Properties and Results

Random Number Generation

Calculation of Probabilities and Percentiles

PARETO DISTRIBUTION

Description

Moments

Computing Table Values

Inferences

Applications

Properties and Results

Random Number Generation

Computation of Probabilities and Percentiles

WEIBULL DISTRIBUTION

Description

Moments

Probabilities, Percentiles, and Moments

Applications

Point Estimation

Properties and Results

Random Number Generation

EXTREME VALUE DISTRIBUTION

Description

Moments

Computing Table Values

Maximum Likelihood Estimators

Applications

Properties and Results

Random Number Generation

CAUCHY DISTRIBUTION

Description

Moments

Computing Table Values

Inference

Applications

Properties and Results

INVERSE GAUSSIAN DISTRIBUTION

Description

Moments

Probabilities, Percentiles, and Moments

One-Sample Inference

Two-Sample Inference

Random Number Generation

RAYLEIGH DISTRIBUTION

Description

Moments

Probabilities, Percentiles, and Moments

Maximum Likelihood Estimator

Relation to Other Distributions

Random Number Generation

BIVARIATE NORMAL DISTRIBUTION

Description

Computing Probabilities

Inferences on Correlation Coefficients

Inferences on the Difference between Two Correlation Coefficients

Test and Confidence Interval for Variances

Some Properties

Random Number Generation

A Computational Algorithm for Probabilities

SOME NONPARAMETRIC METHODS

Distribution of Runs

Sign Test and Confidence Interval for the Median

Wilcoxon Signed-Rank Test and Mann-Whitney U Statistic

Wilcoxon Rank-Sum Test

Quantile Estimation and Nonparametric Tolerance Interval

About the Author

Kalimuthu Krishnamoorthy, Ph.D., is a professor of statistics and SLEMCO Professor of Science at the University of Louisiana at Lafayette. He is an elected fellow of the American Statistical Association and an associate editor of Communications in Statistics. He has published more than 100 articles relating to small sample inference, multivariate analysis, fiducial inference, and statistical methods for exposure data analysis.

About the Series

Statistics: A Series of Textbooks and Monographs

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
MAT029000
MATHEMATICS / Probability & Statistics / General