Exact distribution of a linear combination of a variable and order statistics from the other two variables of a trivariate elliptical random vector as a mixture of skew-elliptical distributions

A Jamalizadeh,H Mahmoodian,N Balakrishnan

doi:10.1016/j.stamet.2009.08.001

Exact distribution of a linear combination of a variable and order statistics from the other two variables of a trivariate elliptical random vector as a mixture of skew-elliptical distributions

A Jamalizadeh, H Mahmoodian + Show 1 more

https://doi.org/10.1016/j.stamet.2009.08.001

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Journal: Statistical Methodology	Publication Date: Aug 13, 2009
Citations: 5

Affiliation: Shahid Sattari University of Aeronautical Engineering, McMaster University

#Skew-elliptical Distribution #Order Statistics + Show 8 more

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Abstract

We consider here a univariate skew-elliptical distribution, which is a special case of the unified multivariate skew-elliptical distribution studied recently by Arellano-Valle and Azzalini (2006) [1]. We then derive the exact distribution of a linear combination of a variable and order statistics from the other two variables in the case of a trivariate elliptical distribution. We show that the cumulative distribution function (cdf) of this linear combination is a mixture of the univariate skew-elliptical distribution functions.

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