A matrix variate inverse Lomax distribution

This study presents the matrix variate inverse Lomax distribution as a generalization of the univariate inverse Lomax distribution and shows that this distribution can be derived by using matrix variate gamma distributions. We study several properties such as cumulative distribution function, marginal distribution of sub-matrix, triangular factorization, moment generating function, Kullback-Liebler divergence, entropies and expected values of the inverse Lomax matrix. We also derive maximum likelihood estimators of the parameters and check their finite sample performance by simulations. Some of these results are expressed in terms of special functions of matrix arguments and zonal polynomials.