Life Distributions: Structure of Nonparametric, Semiparametric, and Parametric Families

Cover
Springer Science & Business Media, 13.10.2007 - 785 Seiten

For over 200 years, practitioners have been developing parametric families of probability distributions for data analysis. More recently, an active development of nonparametric and semiparametric families has occurred. This book includes an extensive discussion of a wide variety of distribution families—nonparametric, semiparametric and parametric—some well known and some not. An all-encompassing view is taken for the purpose of identifying relationships, origins and structures of the various families. A unified methodological approach for the introduction of parameters into families is developed, and the properties that the parameters imbue a distribution are clarified. These results provide essential tools for intelligent choice of models for data analysis. Many of the results given are new and have not previously appeared in print. This book provides a comprehensive reference for anyone working with nonnegative data.

 

Ausgewählte Seiten

Inhalt

Introduction F Parametric Families Basic Examples G Nonparametric Families Basic Examples H Functions of Random Variables I Inverse Distributio...
35
Descriptive
46
A Basic
80
Preface vii
87
Densities
96
Origins
137
Inequalities for Moments
195
A Introduction 217
216
B The Uniform Distribution and OneParameter
475
Additional TwoParameter Extensions of
489
26
496
Covariate Models
533
Competing A Definitions and Notation Risks 541
541
Characterizations Through Coincidences
563
28
577
47
591

Scale Parameters
224
The Exponential
292
Parametric Extensions of the Exponential
309
Gompertz and GompertzMakeham Distributions
362
7
374
22
385
Pareto and F Distributions and Their
399
The
418
Logarithmic
427
451
452
25
461
More About Semiparametric Families 611
610
Some Topics from Probability Theory 635
633
76
695
Some Functional
701
Some Topics from
728
79
737
80
744
733
763
375
765
Subject
771
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Life Distributions: Structure of Nonparametric, Semiparametric, and ...
Albert W. Marshall,Ingram Olkin
Keine Leseprobe verfügbar - 2010
Life Distributions: Structure of Nonparametric, Semiparametric, and ...
Albert W. Marshall,Ingram Olkin
Keine Leseprobe verfügbar - 2007

Häufige Begriffe und Wortgruppen

bathtub hazard rates beta distribution bution Chapter coherent system components condition consequently convolution parameter decreasing defined Definition density f derivative differentiable distri distribution F distribution function Example exponential distribution F distribution F is NBU finite follows from Proposition frailty parameter function F gamma distribution given Gompertz distribution hazard function hazard rate order IHRA increasing hazard rate independent inequality infinitely divisible interval inverse Gaussian distribution Laplace transform Lemma likelihood ratio order log concave log convex log F log F(x mixture monotone NBUE nonnegative random variables notation obtained parameter family Pareto Pareto distribution properties random variable residual life distribution resilience parameter result reverse hazard rate satisfies scale parameter semiparametric family stochastic order survival function test transform Theorem tilt parameter tion totally positive underlying distribution unimodal verified Weibull distribution

Beliebte Passagen

Seite 6 - From a limited experience, for example, of individuals of a species, or of the weather of a locality, we may obtain some idea of the infinite hypothetical population from which our sample is drawn, and so of the probable nature of future samples to which our conclusions are to be applied.
Wird in 13 Büchern von 1925 bis 2007 erwähnt
Seite 3 - Probability is a mathematical discipline with aims akin to those, for example, of geometry or analytical mechanics. In each field we must carefully distinguish three aspects of the theory: (a) the formal logical content, (b) the intuitive background, (c) the applications. The character, and the charm, of the whole structure cannot be appreciated without considering all three aspects in their proper relation.
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Seite iv - Ibrahim: Monte Carlo Methods in Bayesian Computation Coles: An Introduction to Statistical Modeling of Extreme Values Devroye/Lugosi: Combinatorial Methods in Density Estimation Diggle/Ribeiro: Model-based Geostatistics Dudoit/Van der Laan: Multiple Testing Procedures with Applications to Genomics Efromovich: Nonparametric Curve Estimation: Methods, Theory, and Applications Eggermont/LaRiccia: Maximum Penalized Likelihood Estimation, Volume I: Density Estimation Fahrmeir/Tutz: Multivariate Statistical...
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Autoren-Profil (2007)

Albert W. Marshall, Professor Emeritus of Statistics at the University of British Colombia, previously served on the faculty of the University of Rochester and on the staff of the Boeing Scientific Research Laboratories. His fundamental contributions to reliability theory have had a profound effect in furthering its development.

Ingram Olkin is Professor Emeritus of Statistics and Education at Stanford University, after having served on the faculties of Michigan State University and the University of Minnesota. He has made significant contributions in multivariate analysis and in the development of statistical methods in meta-analysis, which has resulted in its use in many applications.

Professors Marshall and Olkin, coauthors of papers on inequalities, multivariate distributions, and matrix analysis, are about to celebrate 50 years of collaborations. Their basic book on majorization has promoted awareness of the subject, and led to new applications in such fields as economics, combinatorics, statistics, probability, matrix theory, chemistry, and political science.

Bibliografische Informationen

TitelLife Distributions: Structure of Nonparametric, Semiparametric, and Parametric Families
Springer Series in Statistics
Engineering (R0)
AutorenAlbert W. Marshall, Ingram Olkin
Ausgabeillustriert
VerlagSpringer Science & Business Media, 2007
ISBN0387684778, 9780387684772
Länge785 Seiten
  
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