Continuous multivariate distributions . Volume 1 Models and applications [[electronic resource] /] / Samuel Kotz, N. Balakrishnan, Norman L. Johnson

• Record Nr.: UNINA9910830699003321
• Autore: Kotz Samuel
• Pubbl/distr/stampa: New York, : John Wiley & Sons, Inc., c2000
• ISBN: 1-280-27277-5; 9786610272778; 0-470-30414-6; 0-471-65403-5; 0-471-72206-5
• Edizione: [2nd ed.]
• Descrizione fisica: 1 online resource (753 p.)
• Collana: Wiley series in probability and statistics
• Altri autori (Persone): JohnsonNorman Lloyd; BalakrishnanN. <1956->
• Disciplina: 519.535
• Soggetti: Distribution (Probability theory); Multivariate analysis
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: "A Wiley-Interscience publication."
• Nota di bibliografia: Includes bibliographical references and indexes.
• Nota di contenuto: Contents; Preface; List of Tables; List of Figures; 44 Systems of Continuous Multivariate Distributions; 1 Introduction; 2 Historical Remarks; 3 Multivariate Generalization of Pearson System; 4 Series Expansions and Multivariate Central Limit Theorems; 5 Translation Systems; 6 Multivariate Linear Exponential-Type Distributions; 7 Sarmanov's Distributions; 8 Multivariate Linnik's Distributions; 9 Multivariate Kagan's Distributions; 10 Generation of Multivariate Nonnormal Random Variables; 11 Fréchet Bounds; 12 Fréchet, Plackett and Mardia's Systems; 13 Farlie-Gumbel-Morgenstern Distributions; 14 Multivariate Phase-Type Distributions15 Chebyshev-Type and Bonferroni Inequalities; 16 Singular Distributions; 17 Distributions with Almost-Lack of Memory; 18 Distributions with Specified Conditionals; 19 Distributions with Given Marginals; 20 Measures of Multivariate Skewness and Kurtosis; Bibliography; 45 Multivariate Normal Distributions; 1 Introduction and Genesis; 2 Definition and Moments; 3 Other Properties; 4 Order Statistics; 5 Evaluation of Multivariate Normal ; Probabilities; 5.1 Reduction Formulas; 5.2 Orthant Probabilities; 5.3 Some Special Cases; 5.4 Approximations; 6 Quadrivariate Normal Orthant Probabilities7 Characterizations; 8 Estimation; 8.1 Estimation of ξ; 8.2 Estimation of V; 8.3 Estimation of Correlations; 8.4 Estimation Under Missing Data; 8.5 Estimation Under Special Structures; 8.6 Estimation of Functions of ξ and V; 9 Tolerance Regions; 10 Truncated Multivariate Normal Distributions; 11 Related Distributions; 12 Mixtures of Multivariate Normal Distributions; 13 Complex Multivariate Normal Distributions; Bibliography; 46 Bivariate and Trivariate Normal Distributions; 1 Definition and Applications; 2 Historical Remarks; 3 Properties and Moments4 Bivariate Normal Integral-Tables and Approximations; 5 Characterizations; 6 Order Statistics; 7 Trivariate Normal Integral; 8 Estimation; 8.1 Bivariate Normal Distribution; 8.2 Trivariate Normal Distributions; 9 Truncated Bivariate and Trivariate Normal Distributions; 10 Dichotomized Variables; 10.1 Tetrachoric Correlation; 10.2 Biserial Correlation; 11 Related Distributions; 11.1 Mixtures of Bivariate Normal Distributions; 11.2 Bivariate Half Normal Distribution; 11.3 Distribution of Ratios; 11.4 ""Bivariate Normal"" Distribution with Centered Normal Conditionals; 11.5 Bivariate Skew-Normal DistributionBibliography; 47 Multivariate Exponential Distributions; 1 Introduction; 2 Bivariate Exponential Distributions; 2.1 Introduction; 2.2 Gumbel's Bivariate Exponentials; 2.3 Freund's Bivariate Exponential (Bivariate Exponential Mixture Distributions); 2.4 Marshall and Olkin's Bivariate Exponential; 2.5 Friday and Patil's Bivariate Exponential; 2.6 Arnold and Strauss' Bivariate Exponential; 2.7 Moran and Downton's Bivariate Exponential; 2.8 Singpurwalla and Youngren's Bivariate Exponential; 2.9 Raftery's Bivariate Exponential; 2.10 Hayakawa's Bivariate Exponential
• Sommario/riassunto: Continuous Multivariate Distributions, Volume 1, Second Edition provides a remarkably comprehensive, self-contained resource for this critical statistical area. It covers all significant advances that have occurred in the field over the past quarter century in the theory, methodology, inferential procedures, computational and simulational aspects, and applications of continuous multivariate distributions. In-depth coverage includes MV systems of distributions, MV normal, MV exponential, MV extreme value, MV beta, MV gamma, MV logistic, MV Liouville, and MV Pareto distributions, as well as MV n