Naradajah, Saralees; Gupta, Arjun K. Linear combination and product of inverted Dirichlet components. (English) Zbl 1149.62304 Natl. Acad. Sci. Lett. 29, No. 11-12, 429-437 (2006). Summary: It is well known that \(X+Y\) has the \(F\) distribution and \(X/(X+Y)\) has the beta distribution when \(X\) and \(Y\) follow the inverted Dirichlet distribution. We derive the exact distributions of \(S= \alpha X+\beta Y\) and \(P= XY\) (involving the Gauss hypergeometric function) and the corresponding moment properties. We also propose approximations for \(S\) and \(P\) and discuss evidence of their robustness based on the powerful Kolmogorov-Smirnov test. MSC: 62E15 Exact distribution theory in statistics 62G10 Nonparametric hypothesis testing 33C90 Applications of hypergeometric functions 62G35 Nonparametric robustness Keywords:inverted Dirichlet distribution; Kolmogorov-Smirnov test; linear combination of random variables; product of random variables PDFBibTeX XMLCite \textit{S. Naradajah} and \textit{A. K. Gupta}, Natl. Acad. Sci. Lett. 29, No. 11--12, 429--437 (2006; Zbl 1149.62304)