Search

The beta (type 1) and inverted beta distributions are of vital importance in science, engineering and economics. In this article, we introduce a matrix variate generalization of the inverted beta distribution. By using linear and quadratic transformations, we obtain several matrix variate distributions including matrix variate generalized beta type 1 distribution. [ABSTRACT FROM AUTHOR]

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]

The complex Wishart distribution has ample applications in science and engineering. In this paper, we give explicit expressions for E (tr (W h)) g (tr (W j)) i and E (tr (W − h)) g (tr (W − j)) i , respectively, for particular values of g, h, i, j, g + h + i + j ≤ 5 , where W follows a complex Wishart distribution. For specific values of g, h, i, j, we first write (tr (W h)) g (tr (W j)) i and (tr (W − h)) g (tr (W − j)) i in terms of zonal polynomials and then by using results on integration evaluate resulting expressions. Several expected values of matrix-valued functions of a complex Wishart matrix have also been derived. [ABSTRACT FROM AUTHOR]

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]