Matrix variate Laplace distribution: Properties and parameter estimation

Year 2018, Volume 11, Issue 1, 32 - 41, 29.06.2018

Y. Murat BULUT

Abstract

In this study, we proposed matrix variate Laplace distribution as a scale mixture of matrix variate normal distribution and exponential distribution. Also, we examine some distributional properties and give maximum likelihood estimators of its parameters based on the EM algorithm.

Keywords

EM algorithm, matrix variate distribution

Matris değişkenli Laplace dağılımı: Özellikleri ve parametre tahmini

Abstract

Bu çalışmada matris değişkenli normal dağılım ve üstel dağılımın ölçek karması olarak matris değişkenli Laplace dağılımı önerilmiştir. Ayrıca önerilen dağılımın özellikleri incelenmiştir ve parametrelerinin tahmini için EM (Expectation-Maximization) algoritmasına dayalı en çok olabilirlik tahmin edicileri verilmiştir. 

Keywords

EM algoritması, matris değişkenli dağılım, parametre tahmini

References

• [1] P. S. Laplace, 1774,Mémoire sur la probabilité des causes par les événemens, Mémoires de Mathématique et de Physique, 6, 621-656. English translation by S. M. Stigler Memoir on the Probability of the Causes of Events in Statistical Science, 1(3), 364-378, 1986.
• [2] G. Ulrich, C. Chen, 1987, A bivariate double exponential distribution and its generalization, ASA Proceedings on Statistical Computing, 127-129.
• [3] D. N. Anderson, 1992, A multivariate linnik distribution, Statistics and Probability Letters, 14, 333-,336.
• [4] T. Eltoft, 2006, On the multivariate Laplace distribution, IEEE Signal Processing Letters, 13(5), 300-303.
• [5] D. F. Andrews, C. L. Mallows, 1974, Scale mixtures of normal distributions, Journal of the Royal Statistical Society: Series B (Methodological), 36(1), 99-102.
• [6] S. Kotz, T. J. Kozubowski, K. Podgorski, 2001, The Laplace Distribution and Generalizations: A Revisit with Applications to Communications, Economics, Engineering and Finance.
• [7] E. G. Sánchez-Manzano, M. A. Gómez-Villegas, J. Marín-Diazaraque, 2002, A matrix variate generalization of the power exponential family of distributions, Communications in Statistics-Theory and Methods, 31(12), 2167-2182.
• [8] M. P. B. Gallaugher, P. D. McNicholas, 2017, Three skewed matrix variate distributions, arXiv:1704.02531v4a.
• [9] A. K. Gupta, D. K. Nagar, 1999, Matrix variate distributions, Chapman and Hall/CRC, Boca Raton.
• [10] A. P. Dempster, N. M. Laird, D. B. Rubin, 1977, Maximum likelihood from incomplete data via the EM algorithm, Journal of the Royal Statistical Society Series B (Methodological), 39(1), 1-38.
• [11] O. E. Barndorff-Nielsen, 1997, Normal inverse gaussian distributions and stochastic volatility modelling, Scandinavian Journal of Statistics, 24(1), 1-13.