An Analytical and Numerical Study of the Linear Combination of the Dirichlet Components

Abstract

The aim of the present paper is to derive the exact distribution and the corresponding moment function of the linear combination S := S₁ + S₂, where (S₁, S₂) has the Dirichlet distribution with positive parameters ₁, ₂ and ₃. We also provide the percentile points associated with the linear combination. Next, a measure of entropy of the linear combination is investigated. Further, we give approximations for this distribution and discuss evidence for their robustness. Finally,
we study the application of the considered linear combination to precipitation data in France and to the financial returns volatility domain.

Key words and phrases. Entropy, Linear combination, Dirichlet distribution, Gauss hypergeometric function.

2010 Mathematics Subject Classification. 60E05, 62E15, 62E17