摘要：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 α X + β Y (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.
关键词：Dirichlet distribution;Gauss hypergeometric function;linear combinations of random variables
