Closure Properties for Heavy-Tailed and Related Distributions

An Overview

Remigijus Leipus, Jonas Šiaulys, Dimitrios Konstantinides

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English

Springer International Publishing AG
15 September 2023

Insurance & actuarial studies; Probability & statistics; Stochastics

Series: SpringerBriefs in Statistics

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.

By: Remigijus Leipus, Jonas Šiaulys, Dimitrios Konstantinides
Imprint: Springer International Publishing AG
Country of Publication: Switzerland
Edition: 1st ed. 2023
Dimensions: Height: 235mm, Width: 155mm,
Weight: 174g
ISBN: 9783031345524
ISBN 10: 3031345525
Series: SpringerBriefs in Statistics
Pages: 92
Publication Date: 15 September 2023
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

- 1. Introduction. - 2. Heavy-Tailed and Related Classes of Distributions. - 3. Closure Properties Under Tail-Equivalence, Convolution, Finite Mixing, Maximum, and Minimum. - 4. Convolution-Root Closure. - 5. Product-Convolution of Heavy-Tailed and Related Distributions. - 6. Summary of Closure Properties.

Remigijus Leipus is a Professor at the Institute of Applied Mathematics, Vilnius University, Lithuania. His research interests include time series analysis, extreme value theory, insurance mathematics, financial econometrics and financial mathematics. Jonas Šiaulys is a Professor at the Institute of Mathematics, Vilnius University, Lithuania. His research interests include probability theory, number theory and insurance mathematics. Dimitrios Konstantinides is a Professor at the Department of Statistics and Actuarial-Financial Mathematics, University of the Aegean, Karlovassi, Greece. His research interests include actuarial mathematics, financial mathematics and risk theory.