Consider an exponential dispersion model (EDM) generated by a probability [mu] on [0,[infinity]) which is infinitely divisible with an unbounded Lévy measure [nu]. The Jørgensen set (i.e., the dispersion parameter space) is then , in which case the EDM is characterized by two parameters:...

While the noncentral Wishart distribution is generally introduced as the distribution of the random symmetric matrix where Y1,...,Yn are independent Gaussian rows in with the same covariance, the present paper starts from a slightly more general definition, following the extension of the...

In this paper an enlargement of the beta family of distributions on (0, 1) is presented. Distributions in this class are characterized as being the laws of certain random continued fractions associated with products of independent random matrices of order 2 whose entries are either constant or...

In this paper, we compute moments of a Wishart matrix variate "U" of the form <openface>E</openface>("Q"("U")) where "Q"("u") is a polynomial with respect to the entries of the symmetric matrix "u", invariant in the sense that it depends only on the eigenvalues of the matrix "u". This gives us in particular the...

The donkey performs a random walk (Xn)n[greater-or-equal, slanted]0 inside a tetrahedron with vertices A1,...,Ad as follows. For r=1,...,d and t=0,1,..., at time dt+r the donkey moves from the point Xdt+r-1 to a point Xdt+r such that the barycentric coordinates of Xdt+r with respect to...

Suppose that the random vector (X1, ..., Xq) follows a Dirichlet distribution on q+ with parameter (p1, ..., pq)[set membership, variant]q+. For f1, ..., fq0, it is well-known that (f1X1+...+fqXq)-(p1+...+pq)=f-p11...f-pqq. In this paper, we generalize this expectation formula...

Let (X1, X2,..., Xq) have the multivariate dirichlet distribution with parameters (p1, p2,..., pq), on the linear space of symmetric (r, r) real matrices. We prove that for a given set of positive numbers f1, f2,..., fq one has . This extends a useful formula already known in dimension r = 1.

Let be a full natural exponential family on which is generated by a self-decomposable probability distribution P. We provide a necessary and sufficient condition on P under which all other elements of are also self-decomposable. Moreover, we show that if is self-decomposable (i.e., composed of...

In an index to the distributions of Mathematical Statistics published in 1961, Frank A. Haight considers, without giving any references, the following distribution: for 0 a 1. We show that these distributions belong to a large class of natural exponential families (in the sense of Carl Morris)...

We split [0,1] in a uniform manner, take the largest of the two intervals thus obtained, split this interval again uniformly, and continue in this fashion ad infinitum. We show that the extremes of this interval converge almost surely to a beta (2,2) random variable.