LEADER 05947nam 22007215 450 001 9910746099003321 005 20240619160646.0 010 $a3-031-34553-3 024 7 $a10.1007/978-3-031-34553-1 035 $a(MiAaPQ)EBC30745207 035 $a(Au-PeEL)EBL30745207 035 $a(DE-He213)978-3-031-34553-1 035 $a(PPN)27273635X 035 $a(CKB)28225227300041 035 $a(EXLCZ)9928225227300041 100 $a20230914d2023 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aClosure Properties for Heavy-Tailed and Related Distributions $eAn Overview /$fby Remigijus Leipus, Jonas ?iaulys, Dimitrios Konstantinides 205 $a1st ed. 2023. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2023. 215 $a1 online resource (99 pages) 225 1 $aSpringerBriefs in Statistics,$x2191-5458 311 08$aPrint version: Leipus, Remigijus Closure Properties for Heavy-Tailed and Related Distributions Cham : Springer,c2023 9783031345524 327 $aIntro -- 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. 327 $a4.2 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. 330 $aThis book provides a compact and systematic overview of closure properties of heavy-tailed and related distributions, including closure under tail equivalence, convolution, finite mixing, maximum, minimum, convolution power and convolution roots, and product-convolution closure. It includes examples and counterexamples that give an insight into the theory and provides numerous references to technical details and proofs for a deeper study of the subject. The book will serve as a useful reference for graduate students, young researchers, and applied scientists. 410 0$aSpringerBriefs in Statistics,$x2191-5458 606 $aProbabilities 606 $aDistribution (Probability theory) 606 $aStochastic models 606 $aActuarial science 606 $aApplied Probability 606 $aDistribution Theory 606 $aProbability Theory 606 $aStochastic Modelling in Statistics 606 $aActuarial Mathematics 606 $aDistribució (Teoria de la probabilitat)$2thub 608 $aLlibres electrònics$2thub 615 0$aProbabilities. 615 0$aDistribution (Probability theory). 615 0$aStochastic models. 615 0$aActuarial science. 615 14$aApplied Probability. 615 24$aDistribution Theory. 615 24$aProbability Theory. 615 24$aStochastic Modelling in Statistics. 615 24$aActuarial Mathematics. 615 7$aDistribució (Teoria de la probabilitat) 676 $a519.24 700 $aLeipus$b Remigijus$01427843 701 $aSiaulys$b Jonas$01427844 701 $aKonstantinides$b Dimitrios$01427845 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910746099003321 996 $aClosure Properties for Heavy-Tailed and Related Distributions$93562765 997 $aUNINA