## Handbook of Statistical Distributions with Applications (Google eBook)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 |

335 | |

345 | |

### Common terms and phrases

approximate beta distribution chi-square distribution click 2-sided click P(X Coefficient of Kurtosis Coefficient of Skewness compute moments compute percentiles compute probabilities compute the p-value Computing Table Values confidence interval confidence level correlation coefficient Critical Values defective items degrees of freedom denominator df dialog box distribution with df Enter the values Example extreme value distribution gamma distribution goto independent integer Kurtosis Let X1 level of significance mean µ Moments Mean noncentrality parameter normal distribution normal population normal random variable null hypothesis numerator df observed value one-sided limits p-value p-value for testing Poisson Power Calculation probability density function probability mass function Properties and Results proportion Random Number rejected required sample sample mean sample size Section select the dialog shape parameter standard deviation standard normal random StatCalc success probability tail probabilities testing H0 tolerance interval tolerance limit two-tail test uniform(0 Values The dialog variance Weibull distribution

### Popular passages

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