Unusual limit theorems for the two tailed Pareto distribution

IF 0.4 4区 数学 Q4 STATISTICS & PROBABILITY
A. Adler, P. Matuła
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引用次数: 3

Abstract

We examine order statistics from a two sided Pareto distribution. It turns out that the smallest two order statistics and the two largest order statistics have very unusual limits. We obtain strong and weak exact laws for the smallest and the largest order statistics. For such statistics we also study the generalized law of the iterated logarithm. For the second smallest and second largest order statistics we prove the central limit theorem even though their second moment is infinite. 2010 AMS Mathematics Subject Classification: Primary: 60F05; Secondary: 60F15.
双尾帕累托分布的异常极限定理
我们从双侧帕累托分布中检验顺序统计量。结果是最小的两个阶统计量和最大的两个阶统计量有非常不寻常的极限。得到了最小阶和最大阶统计量的强、弱精确律。对于这种统计,我们还研究了迭代对数的广义律。对于二阶和二阶统计量,我们证明了中心极限定理,即使它们的二阶矩是无限的。2010 AMS数学学科分类:初级:60F05;二级:60 f15。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
0.70
自引率
0.00%
发文量
0
审稿时长
>12 weeks
期刊介绍: PROBABILITY AND MATHEMATICAL STATISTICS is published by the Kazimierz Urbanik Center for Probability and Mathematical Statistics, and is sponsored jointly by the Faculty of Mathematics and Computer Science of University of Wrocław and the Faculty of Pure and Applied Mathematics of Wrocław University of Science and Technology. The purpose of the journal is to publish original contributions to the theory of probability and mathematical statistics.
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