05947nam 22007215 450 991074609900332120240619160646.03-031-34553-310.1007/978-3-031-34553-1(MiAaPQ)EBC30745207(Au-PeEL)EBL30745207(DE-He213)978-3-031-34553-1(PPN)27273635X(CKB)28225227300041(EXLCZ)992822522730004120230914d2023 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierClosure Properties for Heavy-Tailed and Related Distributions An Overview /by Remigijus Leipus, Jonas Šiaulys, Dimitrios Konstantinides1st ed. 2023.Cham :Springer Nature Switzerland :Imprint: Springer,2023.1 online resource (99 pages)SpringerBriefs in Statistics,2191-5458Print version: Leipus, Remigijus Closure Properties for Heavy-Tailed and Related Distributions Cham : Springer,c2023 9783031345524 Intro -- Preface -- Contents -- Acronyms -- 1 Introduction -- 1.1 An Overview of the Book -- 1.2 Notations and Definitions -- 2 Heavy-Tailed and Related Classes of Distributions -- 2.1 Heavy-Tailed Distributions -- 2.2 Regularly Varying Distributions -- 2.3 Consistently Varying Distributions -- 2.4 Dominatedly Varying Distributions -- 2.5 Long-Tailed Distributions -- 2.6 Exponential-Like-Tailed Distributions -- 2.7 Generalized Long-Tailed Distributions -- 2.8 Subexponential Distributions -- 2.9 Strong Subexponential Distributions -- 2.10 Convolution Equivalent Distributions -- 2.11 Generalized Subexponential Distributions -- 2.12 Bibliographical Notes -- 3 Closure Properties Under Tail-Equivalence, Convolution, Finite Mixing, Maximum, and Minimum -- 3.1 Ruin Probability in the Cramér-Lundberg Risk Model in the Case of Heavy-Tailed Claims -- 3.2 Convolution Closure and Max-Sum Equivalence -- 3.3 Closure Properties for Heavy-Tailed Class of Distributions -- 3.4 Closure Properties for Regularly Varying Class of Distributions -- 3.5 Closure Properties for Consistently Varying Class of Distributions -- 3.6 Closure Properties for Dominatedly Varying Class of Distributions -- 3.7 Closure Properties for Long-Tailed Class of Distributions -- 3.8 Closure Properties for Exponential-Like-Tailed Class of Distributions -- 3.9 Closure Properties for Generalized Long-Tailed Class of Distributions -- 3.10 Closure Properties for Subexponential Class of Distributions -- 3.11 Closure Properties for Strong Subexponential Class of Distributions -- 3.12 Closure Properties for Convolution Equivalent Class of Distributions -- 3.13 Closure Properties for Generalized Subexponential Class of Distributions -- 3.14 Bibliographical Notes -- 4 Convolution-Root Closure -- 4.1 Distribution Classes Closed Under Convolution Roots.4.2 Distribution Classes Not Closed Under Convolution Roots -- 4.3 Bibliographical Notes -- 5 Product-Convolution of Heavy-Tailed and Related Distributions -- 5.1 Product-Convolution -- 5.2 From Light Tails to Heavy Tails Through Product-Convolution -- 5.3 Product-Convolution Closure Properties for Heavy-Tailed Class of Distributions -- 5.4 Product-Convolution Closure Properties for Regularly Varying Class of Distributions -- 5.5 Product-Convolution Closure Properties for Consistently Varying Class of Distributions -- 5.6 Product-Convolution Closure Properties for Dominatedly Varying Class of Distributions -- 5.7 Product-Convolution Closure Properties for Exponential-Like-Tailed Distributions -- 5.8 Product-Convolution Closure Properties for Generalized Long-Tailed Class of Distributions -- 5.9 Product-Convolution Closure Properties for Convolution Equivalent Class of Distributions -- 5.10 Product-Convolution Closure Properties for Generalized Subexponential Class of Distributions -- 5.11 Some Extensions -- 5.12 Bibliographical Notes -- 6 Summary of Closure Properties -- References -- Index.This book provides a compact and systematic overview of closure properties of heavy-tailed and related distributions, including closure under tail equivalence, convolution, finite mixing, maximum, minimum, convolution power and convolution roots, and product-convolution closure. It includes examples and counterexamples that give an insight into the theory and provides numerous references to technical details and proofs for a deeper study of the subject. The book will serve as a useful reference for graduate students, young researchers, and applied scientists.SpringerBriefs in Statistics,2191-5458ProbabilitiesDistribution (Probability theory)Stochastic modelsActuarial scienceApplied ProbabilityDistribution TheoryProbability TheoryStochastic Modelling in StatisticsActuarial MathematicsDistribució (Teoria de la probabilitat)thubLlibres electrònicsthubProbabilities.Distribution (Probability theory).Stochastic models.Actuarial science.Applied Probability.Distribution Theory.Probability Theory.Stochastic Modelling in Statistics.Actuarial Mathematics.Distribució (Teoria de la probabilitat)519.24Leipus Remigijus1427843Siaulys Jonas1427844Konstantinides Dimitrios1427845MiAaPQMiAaPQMiAaPQBOOK9910746099003321Closure Properties for Heavy-Tailed and Related Distributions3562765UNINA