The Generalized Pascal Triangle and the Matrix Variate Jensen-Logistic Distribution

Francisco J. Caro-Lopera, Graciela González-Farías and N. Balakrishnan

Communications in Statistics - Theory and Methods, 2015, vol. 44, issue 13, 2738-2752

Abstract: This article defines the so called Generalized Matrix Variate Jensen-Logistic distribution. The relevant applications of this class of distributions in Configuration Shape Theory consist of a more efficient computation, supported by the corresponding inference. This demands the solution of two important problems: (1) the development of analytical and efficient formulae for their k-th derivatives and (2) the use of the derivatives to transform the configuration density into a polynomial density under some special matrix Kummer relation, indexed in this case by the Jensen-Logistic kernel. In this article, we solve these problems by deriving a simple formula for the k-th derivative of the density function, avoiding the usual partition theory framework and using a generalization of Pascal triangles. Then we apply the results by obtaining the associated Jensen-Logistic Kummer relations and the configuration polynomial density in the setting of Statistical Shape Theory.

Date: 2015
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DOI: 10.1080/03610926.2013.791374

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