Skip to Main Content
Remote Access Theory of Probability and Mathematical Statistics

Theory of Probability and Mathematical Statistics

ISSN 1547-7363(online) ISSN 0094-9000(print)

   
 
 

 

Matrix variate generalized asymmetric Laplace distributions


Authors: Tomasz J. Kozubowski, Stepan Mazur and Krzysztof Podgórski
Journal: Theor. Probability and Math. Statist. 109 (2023), 55-80
MSC (2020): Primary 62H10, 60E05; Secondary 60E10
DOI: https://doi.org/10.1090/tpms/1197
Published electronically: October 3, 2023
MathSciNet review: 4652994
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The generalized asymmetric Laplace (GAL) distributions, also known as the variance/mean-gamma models, constitute a popular flexible class of distributions that can account for peakedness, skewness, and heavier-than-normal tails, often observed in financial or other empirical data. We consider extensions of the GAL distribution to the matrix variate case, which arise as covariance mixtures of matrix variate normal distributions. Two different mixing mechanisms connected with the nature of the random scaling matrix are considered, leading to what we term matrix variate GAL distributions of Type I and II. While Type I matrix variate GAL distribution has been studied before, there is no comprehensive account of Type II in the literature, except for their rather brief treatment as a special case of matrix variate generalized hyperbolic distributions. With this work we fill this gap, and present an account for basic distributional properties of Type II matrix variate GAL distributions. In particular, we derive their probability density function and the characteristic function, as well as provide stochastic representations related to matrix variate gamma distribution. We also show that this distribution is closed under linear transformations, and study the relevant marginal distributions. In addition, we also briefly account for Type I and discuss the intriguing connections with Type II. We hope that this work will be useful in the areas where matrix variate distributions provide an appropriate probabilistic tool for three-way or, more generally, panel data sets, which can arise across different applications.


References [Enhancements On Off] (What's this?)

References

Similar Articles

Retrieve articles in Theory of Probability and Mathematical Statistics with MSC (2020): 62H10, 60E05, 60E10

Retrieve articles in all journals with MSC (2020): 62H10, 60E05, 60E10


Additional Information

Tomasz J. Kozubowski
Affiliation: Department of Mathematics and Statistics, University of Nevada, NV-89557 Reno
Email: tkozubow@unr.edu

Stepan Mazur
Affiliation: Department of Statistics, Örebro University, SE-70182 Örebro, Sweden; and Department of Economics and Statistics, Linnaeus University, SE-35195 Växjö, Sweden
Email: Stepan.Mazur@oru.se

Krzysztof Podgórski
Affiliation: Department of Statistics, Lund University, SE-22007 Lund, Sweden
Email: Krzysztof.Podgorski@stat.lu.se

Keywords: Covariance mixture of Gaussian distributions, distribution theory, generalized asymmetric Laplace distribution, MatG distribution, matrix variate distribution, matrix variate gamma distribution, matrix gamma-normal distribution, matrix variate $t$ distribution, normal variance-mean mixture, variance gamma distribution
Received by editor(s): June 6, 2022
Accepted for publication: January 4, 2023
Published electronically: October 3, 2023
Additional Notes: The second author acknowledges financial support from the internal research grants at Örebro University and from the project “Models for macro and financial economics after the financial crisis” (Dnr: P18-0201) funded by Jan Wallander and Tom Hedelius foundation.
The third author acknowledges financial support of the Swedish Research Council (VR) Grant DNR: 2020-05168.
Article copyright: © Copyright 2023 Taras Shevchenko National University of Kyiv