# Handbook of Statistical Distributions with Applications

#### By **Kalimuthu Krishnamoorthy**

#### Series Editor: **N. Balakrishnan**

Chapman and Hall/CRC – 2006 – 376 pages

Chapman and Hall/CRC – 2006 – 376 pages

In the area of applied statistics, scientists use statistical distributions to model a wide range of practical problems, from modeling the size grade distribution of onions to modeling global positioning data. To apply these probability models successfully, practitioners and researchers must have a thorough understanding of the theory as well as a familiarity with the practical situations. **The Handbook of Statistical Distributions with Applications** is the first reference to combine popular probability distribution models, formulas, applications, and software to assist you in computing probabilities, percentiles, moments, and other statistics.

Presenting both common and specialized probability distribution models, as well as providing applications with practical examples, this handbook offers comprehensive coverage of plots of probability density functions, methods of computing probability and percentiles, algorithms for random number generation, and inference, including point estimation, hypothesis tests, and sample size determination. The book discusses specialized distributions, some nonparametric distributions, tolerance factors for a multivariate normal distribution, and the distribution of the sample correlation coefficient, among others.

Developed by the author, the StatCal software (available for download at www.crcpress.com), along with the text, offers a useful reference for computing various table values. By using the software, you can compute probabilities, parameters, and moments; find exact tests; and obtain exact confidence intervals for distributions, such as binomial, hypergeometric, Poisson, negative binomial, normal, lognormal, inverse Gaussian, and correlation coefficient.

In the applied statistics world, the **Handbook of Statistical Distributions with Applications** is now the reference for examining distribution functions - including univariate, bivariate normal, and multivariate - their definitions, their use in statistical inference, and their algorithms for random number generation.

Quite simply, this book is a masterwork. … an essential resource for anyone who models data, or creates applications which 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

…it seems indeed that the book has a chance of becoming a highly valued practitioner’s reference … .

— *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, Open University, in *Journal of Applied Statistics*, Jan. 2008, Vol. 35, No. 2

In summary, this book can be recommended to statistical practitioners who need a comprehensive yet brief reference on statistical distributions with applications.

— Brian Wiens, Gilead Sciences, Inc., in *The American Statistician*, Nov.2007, Vol. 61, No. 4

INTRODUCTION TO STATCALC

Introduction

of StatCalc

PRELIMINARIES

Random Variables and Expectations

Moments and Other Functions

Some Functions Relevant to Reliability

Model Fitting

Methods of Estimation

Inference

Random Number Generation

Some Special Functions

DISCRETE UNIFORM DISTRIBUTION

Description

Moments

BINOMIAL DISTRIBUTION

Description

Moments

Computing Table Values

Test for the Proportion

Confidence Intervals for the Proportion

A Test for the Difference between Two Proportions

Fisher's Exact Test

Properties and Results

Random Number Generation

Computation of Probabilities

HYPERGEOMETRIC DISTRIBUTION

Description

Moments

Computing Table Values

Point Estimation

Test for the Proportion

Confidence Intervals and Sample Size Calculation

A Test for the Difference between Two Proportions

Properties and Results

Random Number Generation

Computation of Probabilities

POISSON DISTRIBUTION

Description

Moments

Computing Table Values

Point Estimation

Test for the Mean

Confidence Intervals for the Mean

Test for the Ratio of Two Means

Confidence Intervals for the Ratio of Two Means

A Test for the Difference between Two Means

Model Fitting with Examples

Properties and Results

Random Number Generation

Computation of Probabilities

GEOMETRIC DISTRIBUTION

Description

Moments

Computing Table Values

Properties and Results

Random Number Generation

NEGATIVE BINOMIAL DISTRIBUTION

Description

Moments

Computing Table Values

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

Computing Table Values

Inferences

Properties and Results

Random Number Generation

A Computational Algorithm for Probabilities

UNIFORM DISTRIBUTION

Description

Moments

Inferences

Properties and Results

Random Number Generation

NORMAL DISTRIBUTION

Description

Moments

Computing Table Values

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

Computing Table Values

Applications

Properties and Results

Random Number Generation

Computing the Distribution Function

F DISTRIBUTION

Description

Moments

Computing Table Values

Properties and Results

Random Number Generation

A Computational Method for Probabilities

STUDENT'S t DISTRIBUTION

Description

Moments

Computing Table Values

Distribution of the Maximum of Several |t| Variables

Properties and Results

Random Number Generation

A Computational Method for Probabilities

EXPONENTIAL DISTRIBUTION

Description

Moments

Computing Table Values

Inferences

Properties and Results

Random Number Generation

GAMMA DISTRIBUTION

Description

Moments

Computing Table Values

Applications with Some Examples

Inferences

Properties and Results

Random Number Generation

A Computational Method for Probabilities

BETA DISTRIBUTION

Description

Moments

Computing Table Values

Inferences

Applications with an Example

Properties and Results

Random Number Generation

Evaluating the Distribution Function

NONCENTRAL CHI-SQUARE DISTRIBUTION

Description

Moments

Computing Table Values

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

Computing Table Values

Applications

Properties and Results

Random Number Generation

Evaluating the Distribution Function

LAPLACE DISTRIBUTION

Description

Moments

Computing Table Values

Inferences

Applications

Relation to Other Distributions

Random Number Generation

LOGISTIC DISTRIBUTION

Description

Moments

Computing Table Values

Maximum Likelihood Estimators

Applications

Properties and Results

Random Number Generation

LOGNORMAL DISTRIBUTION

Description

Moments

Computing Table Values

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

Computation of Probabilities and Percentiles

PARETO DISTRIBUTION

Description

Moments

Computing Table Value

Inferences

Applications

Properties and Results

Random Number Generation

Computation of Probabilities and Percentiles

WEIBULL DISTRIBUTION

Description

Moments

Computing Table Values

Applications

Point Estimation

Properties and Results

Random Number Generation

Computation of Probabilities and Percentiles

EXTREME VALUE DISTRIBUTION

Description

Moments

Computing Table Values

Maximum Likelihood Estimators

Applications

Properties and Results

Random Number Generation

Computation of Probabilities and Percentiles

CAUCHY DISTRIBUTION

Description

Moments

Computing Table Values

Inference

Applications

Properties and Results

Random Number Generation

Computation of Probabilities and Percentiles

INVERSE GAUSSIAN DISTRIBUTION

Description

Moments

Computing Table Values

One-Sample Inference

Two-Sample Inference

Random Number Generation

Computational Methods for Probabilities and Percentiles

RAYLEIGH DISTRIBUTION

Description

Moments

Computing Table Values

Maximum Likelihood Estimator

Relation to Other Distributions

Random Number Generation

BIVARIATE NORMAL DISTRIBUTION

Description

Computing Table Values

An Example

Inferences on Correlation Coefficients

Inferences on the Difference between Two Correlation Coefficients

Some Properties

Random Number Generation

A Computational Algorithm for Probabilities

DISTRIBUTION OF RUNS

Description

Computing Table Values

Examples

SIGN TEST AND CONFIDENCE INTERVAL FOR THE MEDIAN

Hypothesis Test for the Median

Confidence Interval for the Median

Computing Table Values

An Example

WILCOXON SIGNED-RANK TEST

Description

Moments and an Approximation

Computing Table Values

An Example

WILCOXON RANK-SUM TEST

Description

Moments and an Approximation

Mann-Whitney U Statistic

Computing Table Values

An Example

NONPARAMETRIC TOLERANCE INTERVAL

Description

Computing Table Values

An Example

TOLERANCE FACTORS FOR A MULTIVARIATE NORMAL POPULATION

Description

Computing Tolerance Factors

Examples

DISTRIBUTION OF THE SAMPLE MULTIPLE

CORRELATION COEFFICIENT

Description

Moments

Inferences

Some Results

Random Number Generation

A Computational Method for Probabilities

Computing Table Values

REFERENCES

INDEX

Name: Handbook of Statistical Distributions with Applications (Hardback) – Chapman and Hall/CRC

Description: By Kalimuthu KrishnamoorthySeries Editor: N. Balakrishnan. In the area of applied statistics, scientists use statistical distributions to model a wide range of practical problems, from modeling the size grade distribution of onions to modeling global positioning data. To apply these probability models...

Categories: Statistical Theory & Methods, Probability Theory & Applications, Psychological Methods & Statistics