期刊名称：Pakistan Journal of Statistics and Operation Research
印刷版ISSN：2220-5810
出版年度：2015
卷号：11
期号：3
页码：283-298
DOI：10.18187/pjsor.v11i3.718
语种：English
出版社：College of Statistical and Actuarial Sciences
摘要：A generalization of Laplace distribution with location parameter $\theta$, $\, -\infty<\theta<\infty$, and scale parameter $\phi>0,$ is defined by introducing a third parameter $\alpha>0$ as a shape parameter. One tractable class of this generalization arises when $\alpha$ is chosen such that 1/$\alpha$ is a positive integer. In this article, we derive explicit forms for the moments of order statistics, and mean values of the range, quasi--ranges, and spacings of a random sample corresponded to any member of this class. For values of the shape parameter $\alpha$ equal $1/i, i=1,\dotsb,8$, and sample sizes equal 2(1)15 short tables are computed for the exact mean values of the range, quasi--ranges, and spacings. Means and variances of all order statistics are also tabulated.
其他摘要： A generalization of Laplace distribution with location parameter $\theta$, $\, -\infty<\theta<\infty$, and scale parameter $\phi>0,$ is defined by introducing a third parameter $\alpha>0$ as a shape parameter. One tractable class of this generalization arises when $\alpha$ is chosen such that 1/$\alpha$ is a positive integer. In this article, we derive explicit forms for the moments of order statistics, and mean values of the range, quasi--ranges, and spacings of a random sample corresponded to any member of this class. For values of the shape parameter $\alpha$ equal $1/i, i=1,\dotsb,8$, and sample sizes equal 2(1)15 short tables are computed for the exact mean values of the range, quasi--ranges, and spacings. Means and variances of all order statistics are also tabulated.
关键词：Generalized Laplace distribution; Order statistics; Range; Quasi-ranges; Multinomial expansion
