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.
- 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 iaulys 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.
