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, 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.
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
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