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Statistical Distributions.

Author: C S Forbes; Merran Evans; Nicholas Hastings; Brian Peacock
Publisher: Chicester : Wiley, 2011.
Edition/Format:   eBook : Document : English : 4th edView all editions and formats
Summary:
A new edition of the trusted guide on commonly used statistical distributions Fully updated to reflect the latest developments on the topic, Statistical Distributions, Fourth Edition continues to serve as an authoritative guide on the application of statistical methods to research across various disciplines. The book provides a concise presentation of popular statistical distributions along with the necessary  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Forbes, Catherine.
Statistical Distributions.
Chicester : Wiley, ©2011
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: C S Forbes; Merran Evans; Nicholas Hastings; Brian Peacock
ISBN: 9780470627235 0470627239
OCLC Number: 794326250
Notes: 11.1 variate relationships.
Description: 1 online resource (232 pages)
Contents: Statistical Distributions; Contents; Preface; 1 Introduction; 2 Terms and Symbols; 2.1 PROBABILITY, RANDOM VARIABLE, VARIATE, AND NUMBER; Probabilistic Experiment; Sample Space; Random Variable; Variate; Random Number; 2.2 RANGE, QUANTILE, PROBABILITY STATEMENT, AND DOMAIN; Range; Quantile; Probability Statement; Probability Domain; 2.3 DISTRIBUTION FUNCTION AND SURVIVAL FUNCTION; Distribution Function; Survival Function; 2.4 INVERSE DISTRIBUTION FUNCTION AND INVERSE SURVIVAL FUNCTION; Inverse Survival Function; 2.5 PROBABILITY DENSITY FUNCTION AND PROBABILITY FUNCTION. 2.6 OTHER ASSOCIATED FUNCTIONS AND QUANTITIES3 General Variate Relationships; 3.1 INTRODUCTION; 3.2 FUNCTION OF A VARIATE; 3.3 ONE-TO-ONE TRANSFORMATIONS AND INVERSES; Inverse of a One-to-One Function; 3.4 VARIATE RELATIONSHIPS UNDER ONE-TO-ONE TRANSFORMATION; Probability Statements; Distribution Function; Inverse Distribution Function; Equivalence of Variates; Inverse Function of a Variate; 3.5 PARAMETERS, VARIATE, AND FUNCTION NOTATION; Variate and Function Notation; 3.6 TRANSFORMATION OF LOCATION AND SCALE; 3.7 TRANSFORMATION FROM THE RECTANGULAR VARIATE; 3.8 MANY-TO-ONE TRANSFORMATIONS. Symmetrical Distributions4 Multivariate Distributions; 4.1 JOINT DISTRIBUTIONS; Joint Range; Bivariate Quantile; Joint Probability Statement; Joint Probability Domain; Joint Distribution Function; Joint Probability Density Function; Joint Probability Function; 4.2 MARGINAL DISTRIBUTIONS; Marginal Probability Density Function and Marginal Probability Function; 4.3 INDEPENDENCE; 4.4 CONDITIONAL DISTRIBUTIONS; Conditional Probability Function and Conditional Probability Density Function; Composition; 4.5 BAYES' THEOREM; 4.6 FUNCTIONS OF A MULTIVARIATE; 5 Stochastic Modeling; 5.1 INTRODUCTION. 5.2 INDEPENDENT VARIATES5.3 MIXTURE DISTRIBUTIONS; Finite Mixture; Infinite Mixture of Distributions; 5.4 SKEW-SYMMETRIC DISTRIBUTIONS; 5.5 DISTRIBUTIONS CHARACTERIZED BY CONDITIONAL SKEWNESS; 5.6 DEPENDENT VARIATES; 6 Parameter Inference; 6.1 INTRODUCTION; 6.2 METHOD OF PERCENTILES ESTIMATION; 6.3 METHOD OF MOMENTS ESTIMATION; 6.4 MAXIMUM LIKELIHOOD INFERENCE; Properties of MLEs; Approximate Sampling Distribution for Fixed n; 6.5 BAYESIAN INFERENCE; Marginal Posteriors; 7 Bernoulli Distribution; 7.1 RANDOM NUMBER GENERATION; 7.2 CURTAILED BERNOULLI TRIAL SEQUENCES; 7.3 URN SAMPLING SCHEME. 7.4 NOTE8 Beta Distribution; 8.1 NOTES ON BETA AND GAMMA FUNCTIONS; Definitions; Interrelationships; Special Values; Alternative Expressions; 8.2 VARIATE RELATIONSHIPS; 8.3 PARAMETER ESTIMATION; 8.4 RANDOM NUMBER GENERATION; 8.5 INVERTED BETA DISTRIBUTION; 8.6 NONCENTRAL BETA DISTRIBUTION; 8.7 BETA BINOMIAL DISTRIBUTION; 9 Binomial Distribution; 9.1 VARIATE RELATIONSHIPS; 9.2 PARAMETER ESTIMATION; 9.3 RANDOM NUMBER GENERATION; 10 Cauchy Distribution; 10.1 NOTE; 10.2 VARIATE RELATIONSHIPS; 10.3 RANDOM NUMBER GENERATION; 10.4 GENERALIZED FORM; 11 Chi-Squared Distribution.

Abstract:

A new edition of the trusted guide on commonly used statistical distributions Fully updated to reflect the latest developments on the topic, Statistical Distributions, Fourth Edition continues to serve as an authoritative guide on the application of statistical methods to research across various disciplines. The book provides a concise presentation of popular statistical distributions along with the necessary knowledge for their successful use in data modeling and analysis. Following a basic introduction, forty popular distributions are outlined in individual chapters that ar.

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