# Handbook of Statistical Distributions with Applications

CRC Press, Jun 19, 2006 - Mathematics - 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.

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### Contents

 Preliminaries 9 Discrete Uniform Distribution 29 Binomial Distribution 31 Hypergeometric Distribution 51 Poisson Distribution 71 Geometric Distribution 93 Negative Binomial Distribution 97 Logarithmic Series Distribution 107
 Logistic Distribution 241 Lognormal Distribution 247 Pareto Distribution 257 Weibull Distribution 263 Extreme Value Distribution 269 Cauchy Distribution 275 Inverse Gaussian Distribution 281 Rayleigh Distribution 289

 Continuous Uniform Distribution 115 Normal Distribution 119 ChiSquare Distribution 155 F Distribution 163 Students t Distribution 171 Exponential Distribution 179 Gamma Distribution 185 Beta Distribution 195 Noncentral Chisquare Distribution 207 Noncentral F Distribution 217 Noncentral t Distribution 225 Laplace Distribution 233
 Bivariate Normal Distribution 293 Distribution of Runs 307 Sign Test and Confidence Interval for the Median 311 Wilcoxon SignedRank Test 315 Wilcoxon RankSum Test 319 Nonparametric Tolerance Interval 323 Tolerance Factors for a Multivariate Normal Population 325 Distribution of the Sample Multiple Correlation Coefficient 329 References 335 Index 345 Copyright

### Popular passages

Page 343 - Estimation of the Mean of a Multivariate Normal Distribution," The Annals of Statistics 9, pp.