Abstract
Investigation of various classes of heavy-tailed distributions attracted intense attention from theoreticians and practitioners because of their use in finance and insurance, communication networks, physics, hydrology, etc. Heavy-tailed distributions, whose most popular subclass is a class of regularly varying distributions, are also standard in applied probability when describing claim sizes in insurance mathematics, service times in queueing theory, and lifetimes of particles in branching process theory. In this book, we study the closure property of heavy-tailed and related distribution classes, which usually states that assuming two or more distributions in some specific class, the result of the corresponding operation (e.g. sum-convolution, product-convolution, mixture) belongs to the same class of distributions. The description of closure properties of a given distribution class is not only an interesting mathematical problem. Using closure properties of a given distribution class, one can effectively construct the representatives of the class and understand the mechanisms causing heavy tails in real life.
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Notes
- 1.
As an example, note a nice review of heavy tails’ appearance in flood peak distributions by Merz et al. [130].
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Leipus, R., Šiaulys, J., Konstantinides, D. (2023). Introduction. In: Closure Properties for Heavy-Tailed and Related Distributions. SpringerBriefs in Statistics. Springer, Cham. https://doi.org/10.1007/978-3-031-34553-1_1
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