Abstract
This paper introduces a new family of matrix variate distributions based on the mean-mixture of normal (MMN) models. The properties of the new matrix variate family, namely stochastic representation, moments and characteristic function, linear and quadratic forms as well as marginal and conditional distributions are investigated. Three special cases including the restricted skew-normal, exponentiated MMN and the mixed-Weibull MMN matrix variate distributions are presented and studied. Based on the specific presentation of the proposed model, an EM-type algorithm can be directly implemented for obtaining maximum likelihood estimate of the parameters. The usefulness and practical utility of the proposed methodology are illustrated through two conducted simulation studies and through the Landsat satellite dataset analysis.
Highlights
The skew-normal (SN) distribution, initially introduced by Azzalini [1], has received considerable attention in both theoretical and applied statistics in the past two decades
Remark 1 Referring to representation (4), it is clear that the mean of Y is M + Λ E(W), showing the assumption that the mean of matrix variate mean-mixture of normal (MVMMN) distribution is not fixed for all members of the population
In this experiment, simulated data are generated from a matrix variate normal inverse Gaussian (MVNIG; [20]) distribution with sample sizes N = 50, 100, 500, 1000 and 2000, to compare the performance of three special cases of MVMMN model
Summary
The skew-normal (SN) distribution, initially introduced by Azzalini [1], has received considerable attention in both theoretical and applied statistics in the past two decades. The rSN model, like the original SN one, can describe the skewness of data, it still is not robust in dealing with the outlying observations To cover this drawback, Negarestani et al [6] used the rSN transformation to introduce the family of multivariate mean mixture of normal (MMN) model. Even though the matrix variate SN distribution has many attractive properties, it suffers from robustness in dealing with heavy tailed data and from parameter estimation. Regarding these drawbacks of the matrix variate SN model and considering the aforementioned properties of the MMN family of distributions, the objective of this paper is to propose a family of matrix variate mean-mixture of normal (MVMMN) distributions.
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