### 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.

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PDFDOI: http://dx.doi.org/10.18187/pjsor.v11i3.718

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Copyright (c) 2015 Pakistan Journal of Statistics and Operation Research

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#### Title

##### Computation of Sample Mean Range of the Generalized Laplace Distribution

#### Keywords

##### Generalized Laplace distribution, Order statistics, Range, Quasi-ranges, Multinomial expansion

#### Description

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.

#### Date

##### 2015-09-08

#### Identifier

#### Source

Print ISSN: 1816-2711 | Electronic ISSN: 2220-5810