Akademik Veri Yönetim Sistemi
JOURNAL OF THE KOREAN STATISTICAL SOCIETY, cilt.52, sa.1, ss.185-222, 2023 (SCI-Expanded)
In this paper, we propose a weighted extension of the family of multivariate Generalized Asymmetric Laplace (GAL) distributions. This extension is formed as a variance-mean mixture of the multivariate normal distribution and the weighted gamma distribution. By using the weighted gamma distribution as the mixing distribution, the resulting family of weighted GAL (WGAL) distributions gains an additional parameter to further regulate kurtosis and tail thickness; this is an advantage over the family of GAL distributions for modeling data sets. In particular, this new parameter provides great flexibility in adjusting the kurtosis and tail thickness for some members of the GAL distributions family, since these distributions are the widely used members of the GAL family without any shape parameter regulating kurtosis and tail thickness. After defining the multivariate WGAL distributions family and constructing the probability density function, we give some special cases of the new family and examine various properties of the new distributions, such as linear transformations, conditional distributions, and multivariate kurtosis measure. We study the maximum likelihood (ML) estimation to estimate the parameters and describe an algorithm based on the expectation maximization (EM) principle to obtain the ML estimates. We also provide simulation studies and real data examples to explore the modeling capacity of some distributions belonging to the newly proposed family of distributions.