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 STATCALCIntroduction of StatCalcPRELIMINARIESRandom Variables and ExpectationsMoments and Other FunctionsSome Functions Relevant to ReliabilityModel FittingMethods of EstimationInferenceRandom Number GenerationSome Special FunctionsDISCRETE UNIFORM DISTRIBUTIONDescriptionMomentsBINOMIAL DISTRIBUTIONDescriptionMomentsComputing Table ValuesTest for the ProportionConfidence Intervals for the ProportionA Test for the Difference between Two ProportionsFisher's Exact TestProperties and ResultsRandom Number GenerationComputation of ProbabilitiesHYPERGEOMETRIC DISTRIBUTIONDescriptionMomentsComputing Table ValuesPoint EstimationTest for the ProportionConfidence Intervals and Sample Size CalculationA Test for the Difference between Two ProportionsProperties and ResultsRandom Number GenerationComputation of ProbabilitiesPOISSON DISTRIBUTIONDescriptionMomentsComputing Table ValuesPoint EstimationTest for the MeanConfidence Intervals for the MeanTest for the Ratio of Two MeansConfidence Intervals for the Ratio of Two MeansA Test for the Difference between Two MeansModel Fitting with ExamplesProperties and ResultsRandom Number GenerationComputation of ProbabilitiesGEOMETRIC DISTRIBUTIONDescriptionMomentsComputing Table ValuesProperties and ResultsRandom Number GenerationNEGATIVE BINOMIAL DISTRIBUTIONDescriptionMomentsComputing Table ValuesPoint EstimationA Test for the ProportionConfidence Intervals for the ProportionProperties and ResultsRandom Number GenerationA Computational Method for ProbabilitiesLOGARITHMIC SERIES DISTRIBUTIONDescriptionMomentsComputing Table ValuesInferencesProperties and ResultsRandom Number GenerationA Computational Algorithm for ProbabilitiesUNIFORM DISTRIBUTIONDescriptionMomentsInferencesProperties and ResultsRandom Number GenerationNORMAL DISTRIBUTIONDescriptionMomentsComputing Table ValuesOne-Sample InferenceTwo-Sample InferenceTolerance IntervalsProperties and ResultsRelation to Other DistributionsRandom Number GenerationComputing the Distribution FunctionCHI-SQUARE DISTRIBUTIONDescriptionMomentsComputing Table ValuesApplicationsProperties and ResultsRandom Number GenerationComputing the Distribution FunctionF DISTRIBUTIONDescriptionMomentsComputing Table ValuesProperties and ResultsRandom Number GenerationA Computational Method for ProbabilitiesSTUDENT'S t DISTRIBUTIONDescriptionMomentsComputing Table ValuesDistribution of the Maximum of Several |t| VariablesProperties and ResultsRandom Number GenerationA Computational Method for ProbabilitiesEXPONENTIAL DISTRIBUTIONDescriptionMomentsComputing Table ValuesInferencesProperties and ResultsRandom Number GenerationGAMMA DISTRIBUTIONDescriptionMomentsComputing Table ValuesApplications with Some ExamplesIn
Quite simply, this book is a masterwork. ... an essential resource for anyone who models data, or creates applications which require reference to, or make use of, statistical distribution functions or random variable sampling/generation. The accompanying PC program is a true application in its own right, neat, tidy, and very, very useful. To have this and the book represents a unique reference work. ... easily understandable by undergraduate as well as graduate scientists and statisticians ... an essential part of the toolkit for professionals working in the quantitative sciences ... a remarkable achievement for the author who so obviously has taken great care over many years to assemble and perfect the software and reference work. This is a book worthy of a prize. -- Paul Barrett, University of Auckland, New Zealand !it seems indeed that the book has a chance of becoming a highly valued practitioner's reference ! . -- Journal of the Royal Statistical Society I recommend the StatCalc software as a useful quick way to obtain and/or check (relative) simple statistical calculations, and the book as its accompanying manual ... many statisticians might find StatCalc a handy addition to their computer desktops, particularly (in my case) with teaching in mind! -- M.C. Jones, Open University, in Journal of Applied Statistics, Jan. 2008, Vol. 35, No. 2 In summary, this book can be recommended to statistical practitioners who need a comprehensive yet brief reference on statistical distributions with applications. -- Brian Wiens, Gilead Sciences, Inc., in The American Statistician, Nov.2007, Vol. 61, No. 4