JOURNAL OF THE JAPAN STATISTICAL SOCIETY
Online ISSN : 1348-6365
Print ISSN : 1882-2754
ISSN-L : 1348-6365
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Exact and Approximate Distributions for the Linear Combination of Inverted Dirichlet Components
Arjun K. GuptaSaralees Nadarajah
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2006 Volume 36 Issue 2 Pages 225-236

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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.

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© 2006 Japan Statistical Society
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