Computation of Sample Mean Range of the Generalized Laplace Distribution

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.