Limit properties for ratios of order statistics from exponentials

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• 作者：Yong Zhang ; Xue Ding
• 关键词：exponential distribution ; order statistics ; strong law of large numbers ; central limit theorem ; law of iterated logarithm
• 刊名：Journal of Inequalities and Applications
• 出版年：2017
• 出版时间：December 2017
• 年：2017
• 卷：2017
• 期：1
• 全文大小：1355KB
• 刊物主题：Analysis; Applications of Mathematics; Mathematics, general;
• 出版者：Springer International Publishing
• ISSN：1029-242X
• 卷排序：2017

文摘

In this paper, we study the limit properties of the ratio for order statistics based on samples from an exponential distribution and obtain the expression of the density functions, the existence of the moments, the strong law of large numbers for \(R_{nij}\) with \(1\leq i< j< m_{n}=m\). We also discuss other limit theorems such as the central limit theorem, the law of iterated logarithm, the moderate deviation principle, the almost sure central limit theorem for self-normalized sums of \(R_{nij}\) with \(2\leq i< j< m_{n}=m\).