Matrix variate skew laplace distribution

Abstract

In this study, we introduce a matrix variate skew Laplace distribution as a variance-mean mixture of the matrix variate normal and the scale inverse gamma distribution. The proposed distribution is a generalization of the multivariate skew Laplace distribution studied by [1]. We explore some distributional properties of the proposed distribution such as the probability density function and the characteristic function. Also, we study the estimation of the parameters and give an EM algorithm to obtain the estimates of the parameters. Then, we give a small simulation study to illustrate the performance of the proposed EM algorithm for finding the estimates.

Keywords

• EM Algorithm
• Matrix Variate Distribution
• Normal Variance-Mean Mixture
• Skew Distribution
• Multivariate Laplace Distribution

References

1. [1] Arslan O. An alternative multivariate skew laplace distribution. Statistical Papers 2010;51:865887. [CrossRef]
2. [2] Barndorff-Nielsen O. Exponentially decreasing distributions for logarithm of particle size. Proc Roy Scand Land 1977;353:401419. [CrossRef]
3. [3] Barndorff-Nielsen O. Hyperbolic distributions and distributions on hyperbolae. Scandinavian J Stat 1978;5:151157.
4. [4] Gallaugher MP, McNicholas PD. Three skewed matrix variate distributions. Stat Probab Lett 2019;145:103109. [CrossRef]
5. [5] Lange K, Sinsheimer JS. Normal/independent distributions and their applications in robust regression. J Comput Graph Stat 1993;2:175198. [CrossRef]
6. [6] Gomez-Sanchez-Manzano E, Gomez-Villegas MA, Marin JM. Multivariate exponenrtial power distributions as mixtures of normal distributions with bayesian applications. Commun Stat Theory Mehods 2008;37(6):972985. [CrossRef]
7. [7] Kozubowski TJ, Podgorski K. A multivariate and asymmetric generalization of laplace distribution. Comput Stat 2000;15:531540. [CrossRef]
8. [8] Fang KT, Kotz S, Ng KW. Symmetric multivariate and related distributions. London: Chapman and Hall; 1990. [CrossRef]

9. [9] Sanchez-Manzano EG, Gomez-Villegas MA, Marin-Diazaraque J. A matrix variate generalization of the power exponential family of distribution. Commun Stat Theory Methods 2002;31:21672182. [CrossRef]
10. [10] Yurchenko, Y. Matrix variate and tensor variate Laplace distributions, arxiv, 2021:arXiv:2104.05669.
11. [11] Kozubowski T, Mazur S, Podgorski, K. Matrix Variate Generalized Laplace Distributions (Working Paper 7/2022) Available at: https://swopec.hhs.se/oruesi/abs/oruesi2022_007.htm Accessed on May 21, 2024.
12. [12] Gallaugher MPB, McNicholas PDA. matrix variate skew-t distribution. Stat 2017;6:160170. [CrossRef]
13. [13] Gallaugher MPB, McNicholas PD. Finite mixtures of skewed matrix variate distributions. Pattern Recogn 2018;80:8393. [CrossRef]