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2nd Edition

Handbook of Statistical Distributions with Applications




ISBN 9781498741491
Published October 23, 2015 by Chapman and Hall/CRC
398 Pages - 38 B/W Illustrations

 
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Book 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.

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

...
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Author(s)

Biography

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.

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