J. Japan Statist. Soc., Vol. 36 (No. 2), pp. 225-236, 2006

Exact and Approximate Distributions for the Linear Combination of Inverted Dirichlet Components

Arjun K. Gupta and Saralees Nadarajah

Abstract. It is well known that X + Y has the F distribution when X and Y follow the inverted Dirichlet distribution. In this paper, we derive the exact distribution of the general form αX + βY (involving the Gauss hypergeometric function) and the corresponding moment properties. We also propose approximations and discuss evidence of their robustness based on the powerful Kolmogorov-Smirnov test. The work is motivated by real-life examples in quality and reliability engineering.

Key words and phrases: Dirichlet distribution, Gauss hypergeometric function, linear combinations of random variables.

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