Characterization of tail distributions based on record values by using the Beurling’s Tauberian theorem

被引：0
作者：
Mohamed El Arrouchi
机构：
[1] Ibn Tofail University,Department of Mathematics, Faculty of Sciences
来源：
Extremes | 2017年 / 20卷
关键词：
Beurling’s tauberian theorem; Regular variation; Self-neglecting; Record values; 26A12; 40E05; 62G30;
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学科分类号：
摘要：
In this paper, we mainly investigate the converse of a well-known theorem proved by Shorrock (J. Appl. Prob. 9, 316–326 1972b), which states that the regular variation of tail distribution implies a non-degenerate limit for the ratios of the record values. Specifically, the converse is proved by using Beurling extension of Wiener’s Tauberian theorem. This equivalence is extended to the Weibull and Gumbel max-domains of attraction.
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页码：111 / 120
页数：9
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