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We introduce a quantile-based multivariate log-normal distribution, providing a new multivariate skewed distribution with positive support. The parameters of this distribution are interpretable in terms of quantiles of marginal distributions and associations between pairs of variables, a desirable feature for statistical modeling purposes. We derive statistical properties of the quantile-based multivariate log-normal distribution involving the transformations, closed-form expressions for the mixed moments, expected value, covariance matrix, mode, Shannon entropy, and Kullback–Leibler divergence. We also present results on marginalization, conditioning, and independence. Additionally, we discuss parameter estimation and verify its performance through simulation studies. We evaluate the model fitting based on Mahalanobis-type distances. An application to children data is presented. [ABSTRACT FROM AUTHOR]

In this article, we generalize the univariate Macdonald distribution to the matrix case and give its derivation using matrix variate gamma distribution. We study several properties such as cumulative distribution function, marginal distribution of submatrix, triangular factorization, moment generating function, and expected values of several functions of the Macdonald matrix. Some of these results are expressed in terms of special functions of matrix arguments and zonal polynomials. [ABSTRACT FROM PUBLISHER]

In this article, we define a four parameter bivariate distribution whose marginal distributions are inverted beta and gamma. For this distribution, we derive results such as product moments, correlation coefficient, marginal and conditional distributions, distributions of sum, product and quotient, information matrix, and entropies. We also deal with the problem of estimation of parameters. [ABSTRACT FROM AUTHOR]