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[null,"1.","Record Nr.",null,"UNINA9910746099003321"]
[null,null,"Autore",null,"Leipus Remigijus"]
[null,null,"Titolo",null,"Closure Properties for Heavy-Tailed and Related Distributions : An Overview / / by Remigijus Leipus, Jonas Šiaulys, Dimitrios Konstantinides"]
[null,null,"Pubbl/distr/stampa",null,"Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2023"]
[null,null,"ISBN",null,"3-031-34553-3"]
[null,null,"Edizione",null,"[1st ed. 2023.]"]
[null,null,"Descrizione fisica",null,"1 online resource (99 pages)"]
[null,null,"Collana",null,"SpringerBriefs in Statistics, , 2191-5458"]
[null,null,"Disciplina",null,"519.24"]
[null,null,"Soggetti",null,"Probabilities"]
[{"$nulls":4},"Distribution (Probability theory)"]
[{"$nulls":4},"Stochastic models"]
[{"$nulls":4},"Actuarial science"]
[{"$nulls":4},"Applied Probability"]
[{"$nulls":4},"Distribution Theory"]
[{"$nulls":4},"Probability Theory"]
[{"$nulls":4},"Stochastic Modelling in Statistics"]
[{"$nulls":4},"Actuarial Mathematics"]
[{"$nulls":4},"Distribució (Teoria de la probabilitat)"]
[{"$nulls":4},"Llibres electrònics"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[{"$nulls":3},"Livello bibliografico","Monografia"]
[null,null,"Nota di contenuto",null,"Intro -- Preface -- Contents -- Acronyms -- 1 Introduction -- 1.1 An Overview of the Book -- 1.2 Notations and Definitions -- 2 Heavy-Tailed and Related Classes of Distributions -- 2.1 Heavy-Tailed Distributions -- 2.2 Regularly Varying Distributions -- 2.3 Consistently Varying Distributions -- 2.4 Dominatedly Varying Distributions -- 2.5 Long-Tailed Distributions -- 2.6 Exponential-Like-Tailed Distributions -- 2.7 Generalized Long-Tailed Distributions -- 2.8 Subexponential Distributions -- 2.9 Strong Subexponential Distributions -- 2.10 Convolution Equivalent Distributions -- 2.11 Generalized Subexponential Distributions -- 2.12 Bibliographical Notes -- 3 Closure Properties Under Tail-Equivalence, Convolution, Finite Mixing, Maximum, and Minimum -- 3.1 Ruin Probability in the Cramér-Lundberg Risk Model in the Case of Heavy-Tailed Claims -- 3.2 Convolution Closure and Max-Sum Equivalence -- 3.3 Closure "]
[{"$nulls":4},"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."]
[{"$nulls":4},"4.2 Distribution Classes Not Closed Under Convolution Roots -- 4.3 Bibliographical Notes -- 5 Product-Convolution of Heavy-Tailed and Related Distributions -- 5.1 Product-Convolution -- 5.2 From Light Tails to Heavy Tails Through Product-Convolution -- 5.3 Product-Convolution Closure Properties for Heavy-Tailed Class of Distributions -- 5.4 Product-Convolution Closure Properties for Regularly Varying Class of Distributions -- 5.5 Product-Convolution Closure Properties for Consistently Varying Class of Distributions -- 5.6 Product-Convolution Closure Properties for Dominatedly Varying Class of Distributions -- 5.7 Product-Convolution Closure Properties for Exponential-Like-Tailed Distributions -- 5.8 Product-Convolution Closure Properties for Generalized Long-Tailed Class of Distributions -- 5.9 Product-Convolution Closure Properties for Convolution Equivalent Class of Distributions -- 5.10 Product-Convolution Closure Properties for Generalized Subexponential Class of Distributions -- 5.11 Some Extensions -- 5.12 Bibliographical Notes -- 6 Summary of Closure Properties -- References -- Index."]
[{"$nulls":3},"Sommario/riassunto","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."]