Properties of the Bellman Gamma Distribution

2000 Mathematics Subject Classification: 62H10.

The Bellman gamma distribution is a matrix variate distribution, which is a generalization of the Wishart distribution. In practice it arises as a distribution of the empirical normal covariance matrix for samples with monotone missing data. The exact distributions of determinants and quotient of determinants of some submatrices of Bellman gamma distributed random matrices are obtained. The method, considered in this paper, gives the possibility to derive the distribution of products and quotient of products of principal minors of a Bellman gamma matrix, and in particular, of a Wishart matrix.