HANDBOOK OF STATISTICAL DISTRIBUTIONS WITH APPLICATIONS, 2ND EDITION

• 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

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.

Features
• Presents numerous statistical tests and interval estimation procedures, aiding you in choosing the proper statistical methods to analyze your data
• Incorporates more than 135 practical examples that help you understand how to apply the results to real-world problems
• Shows how to implement the methods using the updated PC calculatorStatCalc
• Includes R codes for calculating various distributions, such as gamma, Weibull, logistic, normal with censored data, exponential, and Pareto
• Provides the StatCalc software and R codes on the author’s website

Author(s) Bio
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 ofCommunications 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.