04778nam a22004815i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118041000800153050001200161050001400173050001200187072001700199072002300216082001500239100003300254245015700287260004600444264004600490300004400536336002600580337002600606338003600632347002400668490004600692505115200738520202501890650001703915650002903932650001903961650001703980650005103997650003604048700002804084710003404112773002004146776003604166830004604202856004804248978-0-387-68477-2DE-He21320141014113431.0cr nn 008mamaa100301s2007 xxu| s |||| 0|eng d a97803876847727 a10.1007/978-0-387-68477-22doi aeng 4aTA169.7 4aT55-T55.3 4aTA403.6 7aTGPR2bicssc 7aTEC0320002bisacsh04a658.562231 aMarshall, Albert W.eauthor.10aLife Distributionsh[electronic resource] :bStructure of Nonparametric, Semiparametric, and Parametric Families /cby Albert W. Marshall, Ingram Olkin. 1aNew York, NY :bSpringer New York,c2007. 1aNew York, NY :bSpringer New York,c2007. aXX, 782 p. 138 illus.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aSpringer Series in Statistics,x0172-73970 aBasics -- Preliminaries -- Ordering Distributions: Descriptive Statistics -- Mixtures -- Nonparametric Families -- Nonparametric Families: Densities and Hazard Rates -- Nonparametric Families: Origins in Reliability Theory -- Nonparametric Families: Inequalities for Moments and Survival Functions -- Semiparametric Families -- Semiparametric Families -- Parametric Families -- The Exponential Distribution -- Parametric Extensions of the Exponential Distribution -- Gompertz and Gompertz-Makeham Distributions -- The Pareto and F Distributions and Their Parametric Extensions -- Logarithmic Distributions -- The Inverse Gaussian Distribution -- Distributions with Bounded Support -- Additional Parametric Families -- Models Involving Several Variables -- Covariate Models -- Several Types of Failure: Competing Risks -- More About Semi-parametric Families -- Characterizations Through Coincidences of Semiparametric Families -- More About Semiparametric Families -- Complementary Topics -- Some Topics from Probability Theory -- Convexity and Total Positivity -- Some Functional Equations -- Gamma and Beta Functions -- Some Topics from Analysis. aFor 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 familiesâ€”nonparametric, semiparametric and parametricâ€”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. 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. 0aEngineering. 0aMathematical statistics. 0aSystem safety.14aEngineering.24aQuality Control, Reliability, Safety and Risk.24aStatistical Theory and Methods.1 aOlkin, Ingram.eauthor.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z9780387203331 0aSpringer Series in Statistics,x0172-739740uhttp://dx.doi.org/10.1007/978-0-387-68477-2