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 are complete with related facts and formulas. Reflecting the latest changes and trends in statistical distribution theory, the Fourth Edition features:
A new chapter on queuing formulas that discusses standard formulas that often arise from simple queuing systems
Methods for extending independent modeling schemes to the dependent case, covering techniques for generating complex distributions from simple distributions
New coverage of conditional probability, including conditional expectations and joint and marginal distributions
Commonly used tables associated with the normal (Gaussian), student-t, F and chi-square distributions
Additional reviewing methods for the estimation of unknown parameters, such as the method of percentiles, the method of moments, maximum likelihood inference, and Bayesian inference
Statistical Distributions, Fourth Edition is an excellent supplement for upper-undergraduate and graduate level courses on the topic. It is also a valuable reference for researchers and practitioners in the fields of engineering, economics, operations research, and the social sciences who conduct statistical analyses.
1 Introduction. 2 Terms and Symbols. 2.1 Probability, Random Variable, Variate and Number. 2.2 Range, Quantile, Probability and Domain. 2.3 Distribution Function and Survival Function. 2.4 Inverse Distribution and Inverse Survival Function. 2.5 Probability Density Function and Probability Function. 2.6 Other Associated Functions and Quantities. 3 General Variate Relationships. 3.1 Introduction. 3.2 Function of a Variate. 3.3 One-to-One Transformations and Inverses. 3.4 Variate Relationships Under One-to-One Transformation. 3.5 Parameters, Variate, and Function Notation. 3.6 Transformation of Location and Scale. 3.7 Transformation from the Rectangular Variate. 3.8 Many-to-One Transformations. 4 Multivariate Distributions. 4.1 Joint Distributions. 4.2 Marginal Distributions. 4.3 Independence. 4.4 Conditional Distributions. 4.5 Bayes' Theorem. 4.6 Functions of a Multivariate. 5 Stochastic Modeling. 5.1 Introduction. 5.2 Independent Variates. 5.3 Mixture Distributions. 5.4 Skew-Symmetric Distributions. 5.5 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. 6.5 Bayesian Inference. 7 Bernoulli Distribution. 7.1 Random Number Generation. 7.2 Curtailed Bernoulli Trial Sequences. 7.3 Urn Sampling Scheme. 7.4 Note. 8 Beta Distribution. 8.1 Notes on Beta and Gamma Functions. 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. 11.1 Variate Relationships. 11.2 Random Number Generation. 11.3 Chi Distribution. 12 Chi-Squared (Noncentral) Distribution. 12.1 Variate Relationships. 13 Dirichlet Distribution. 13.1 Variate Relationships. 13.2 Dirichlet Multinomial Distribution. 14 Empirical Distribution Function. 14.1 Estimation from Uncensored Data. 14.2 Estimation from Censored Data. 14.3 Parameter Estimation. 14.4 Example. 14.5 Graphical Method for the Modified Order-Numbers. 14.6 Model Accuracy. 15 Erlang Distribution. 15.1 Variate Relationships. 15.2 Parameter Estimation. 15.3 Random Number Generation. 16 Error Distribution. 16.1 Note. 16.2 Variate Relationships. 17 Exponential Distribution. 17.1 Note. 17.2 Variate Relationships. 17.3 Parameter Estimation. 17.4 Random Number Generation. 18 Exponential Family. 18.1 Members of the Exponential Family. 18.2 Univariate One-Parameter Exponential Family. 18.3 Estimation. 18.4 Generalized Exponential Distributions. 19 Extreme Value (Gumbel) Distribution. 19.1 Note. 19.2 Variate Relationships. 19.3 Parameter Estimation. 19.4 Random Number Generation. 20 F (Variance Ratio) or Fisher{ Snedecor Distribution. 20.1 Variate Relationships. 21 F (Noncentral) Distribution. 21.1 Variate Relationships. 22 Gamma Distribution. 22.1 Variate Relationships. 22.2 Parameter Estimation. 22.3 Random Number Generation. 22.4 Inverted Gamma Distribution. 22.5 Normal Gamma Distribution. 22.6 Generalized Gamma Distribution. 22.6.1 Variate Relationships. 23 Geometric Distribution. 23.1 Notes. 23.2 Variate Relationships. 23.3 Random Number Generation. 24 Hypergeometric Distribution. 24.1 Note. 24.2 Variate Relationships. 24.3 Parameter Estimation. 24.4 Random Number Generation. 24.5 Negative Hypergeometric Distribution. 24.6 Generalized Hypergeometric (Series) Distribution. 25 Inverse Gaussian (Wald) Distr
(0 Comentarios)
