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

详细信息    查看全文

• 作者：Mohamed El Arrouchi
• 关键词：Beurling’s tauberian theorem ; Regular variation ; Self ; neglecting ; Record values
• 刊名：Extremes
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：20
• 期：1
• 页码：111-120
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Statistics, general; Quality Control, Reliability, Safety and Risk; Civil Engineering; Hydrogeology; Environmental Management; Statistics for Business/Economics/Mathematical Finance/Insurance;
• 出版者：Springer US
• ISSN：1572-915X
• 卷排序：20

文摘

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.