On relative stability and weighted laws of large numbers

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• 作者：André Adler ; Anthony G. Pakes
• 关键词：Relative stability ; Weighted laws of large numbers ; Regular variation ; Quotients of order statistics
• 刊名：Extremes
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：20
• 期：1
• 页码：1-31
• 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

Weighted laws of large numbers are established for components which are independent copies of a positive relatively stable law and the weights comprise a regularly varying sequence. The index of regular variation of the weights must be at least −1 for a weak law and be exactly −1 for a strong law. Consideration is given to the special case where the truncated moment function is proportional to the logarithm, a case arising from quotients of independent random variables and quotients of successive order statistics. Closure of the class of positive relatively stable laws under independent multiplication (i.e, Mellin convolution) is reprised and tail equivalences are extended.