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Abstract

 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.

Keywords

Generalized Laplace distribution Order statistics Range Quasi-ranges Multinomial expansion

Article Details

Author Biography

Kamal Samy Selim, Cairo University

Department of Computational Social Sciences

Faculty of Economics and Political Science,

Associate professor

How to Cite
Selim, K. S. (2015). Computation of Sample Mean Range of the Generalized Laplace Distribution. Pakistan Journal of Statistics and Operation Research, 11(3), 283-298. https://doi.org/10.18187/pjsor.v11i3.718