On the Parameter Estimation of the Asymmetric Multivariate Laplace Distribution

Abstract

This article examines a family of three-parameter multivariate Laplace distributions ML _p (a, μ, Σ) which is closed under constant shifts. Parameter vectors a and μ are called shift and shape parameter, respectively, positive definite p × p-matrix Σ is a scale parameter. The first three moments are derived and used for estimating the parameters. The behavior of the obtained estimates is explored in a simulation experiment.

Keywords:

• Method of moments
• Multivariate Laplace distribution
• Multivariate moments
• Parameter estimation
• Skewness

Mathematics Subject Classification:

• 62H12
• 62H05

Acknowledgments

I am grateful to the referee whose suggestions have improved the presentation of this article. I am also thankful to Professor Tnu Kollo for advice and discussions on the topic and to the Estonian Research Foundation for support through grants 5686 and 7435.