A Multivariate and Asymmetric Generalization of Laplace Distribution

Tomasz J. Kozubowski and Krzysztof Podgórski
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Tomasz J. Kozubowski: The University of Tennessee at Chattanooga
Krzysztof Podgórski: Indiana University — Purdue University

Computational Statistics, 2000, vol. 15, issue 4, No 5, 540 pages

Abstract: Summary Consider a sum of independent and identically distributed random vectors with finite second moments, where the number of terms has a geometric distribution independent of the summands. We show that the class of limiting distributions of such random sums, as the number of terms converges to infinity, consists of multivariate asymmetric distributions that are natural generalizations of univariate Laplace laws. We call these limits multivariate asymmetric Laplace laws. We give an explicit form of their multidimensional densities and show representations that effectively facilitate computer simulation of variates from this class. We also discuss the relation to other formerly considered classes of distributions containing Laplace laws.

Keywords: Bessel function; geometric compound; geometric stable law; heavy tailed modeling; elliptically contoured distribution; mixture; random summation; simulation (search for similar items in EconPapers)
Date: 2000
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Citations: View citations in EconPapers (9)

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DOI: 10.1007/PL00022717

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