The multivariate Kummer-Beta and multivariate Kummer-Gamma families of distributions have been proposed and studied recently by Ng and Kotz. These distributions are extensions of Kummer-Beta and Kummer-Gamma distributions. In this article we propose and study matrix variate generalizations of multivariate Kummer-Beta and multivariate Kummer-Gamma families of distributions
We define the first match function T n : C n → {1, . . . , n} where C is a finite alphabet. For two copies of x n 1 ∈ C n , this function gives the minimum number of steps one has to slide one copy of x n 1 to get a match with the other one. For ergodic positive entropy processes, Saussol and coauthors proved the almost sure convergence of T n /n. We compute the large deviation properties of this function. We prove that this limit is related to the Rényi entropy function, which is also proved to exist. Our results hold under a condition easy to check which defines a large class of processes. We provide some examples.
In this article we propose matrix variate Kummer-Gamma distribution which is an extension of matrix variate Gamma distribution. Several properties of this distribution have been studied. Distributional results on randorn quadratic forms involving Kummer-Gamma matrix have also been derived.
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