Asymptotic expansions of convolutions of regularly varying distributions
| Autor: | William P. McCormick, Philippe Barbe |
|---|---|
| Rok vydání: | 2005 |
| Předmět: |
050208 finance
General Mathematics 05 social sciences Mathematical analysis Convolution power Convolution of probability distributions 01 natural sciences Circular convolution Convolution 010104 statistics & probability Heavy-tailed distribution 0502 economics and business 0101 mathematics Convolution theorem Asymptotic expansion Random variable Mathematics |
| Zdroj: | Journal of the Australian Mathematical Society. 78:339-371 |
| ISSN: | 1446-8107 1446-7887 |
| DOI: | 10.1017/s1446788700008570 |
| Popis: | In this paper we derive precise tail-area approximations for the sum of an arbitrary finite number of independent heavy-tailed random variables. In order to achieve second-order asymptotics, a mild regularity condition is imposed on the class of distribution functions with regularly varying tails.Higher-order asymptotics are also obtained when considering asemiparametric subclass of distribution functions with regularly varying tails. These semiparametric subclasses are shown to be closed under convolutions and a convolution algebra is constructed to evaluate the parameters of a convolution from the parameters of the constituent distributions in the convolution. A Maple code is presented which does this task. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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