Handbook of Statistical Distributions with Applications

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.

Table of Contents:
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