A Novel Approach to Handling the Non-Central Dirichlet Distribution

Carlo Orsi

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arXiv · 2108.08947

A Novel Approach to Handling the Non-Central Dirichlet Distribution

Carlo Orsi

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Abstract

In the present paper new insights into the study of the Non-central Dirichlet distribution are provided. This latter is the analogue of the Dirichlet distribution obtained by replacing the Chi-Squared random variables involved in its definition by as many non-central ones. Specifically, a novel approach to tackling the analysis of this model is introduced based on a simple conditional density together with a suitable transposition into the non-central framework of a characterizing property of independent Chi-Squared random variables. This approach thus enables to remedy the undeniable mathematical complexity of the joint density function of such distribution by paving the way towards achieving a new attractive stochastic representation as well as a surprisingly simple closed-form expression for its mixed raw moments.

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Carlo Orsi. 2021-08-19. A Novel Approach to Handling the Non-Central Dirichlet Distribution. https://arxiv.org/abs/2108.08947

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