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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共 15 条
  • [1] Bingham NH(2014)Beurling slow and regular variation Trans. London Math. Soc. 1 2956-1725
  • [2] Ostaszewski AJ(1952)The distribution and frequency of record values J. Roy. Statist. Soc. Ser. B 14 220228-1736
  • [3] Chandler KN(1964)Extremal processes Ann. Math. Statist. 35 1718-53
  • [4] Dwass M(1964)On extreme order statistics Ann. Math. Statist. 35 1726-172
  • [5] Lamperti I(2002)Tauberian Theorems and Limit Distributions for Upper Order Statistics Publications de l’Institut de Mathématiques de Belgrade 71 41-8
  • [6] Lanzinger H(1972)On a general Tauberian theorem Proc. Amer. Math. Soc. 36 167-223
  • [7] Stadtmüller U(1963)Uber das asymptotische Verhalten der Rand- und Zentralglieder einer Variationsreihe Publ. Math. Inst. Hung. Acad. Sci 8 463-326
  • [8] Moh TT(1972)A limit theorem for inter-record times J. Appl. Prob. 9 219-292
  • [9] Rossberg HJ(1972)On record values and record times J. Appl. Prob. 9 316-122
  • [10] Shorrock RW(1975)Convergence in distribution of quotients of order statistics Stoch. Proc. Appl. 3 287-undefined
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