Exact distribution of random weighted convolution of some beta distributions through an integral transform

Abstract

We give the exact distribution of the average of n independent beta random variables weighted by the selected cuts of (0,1) by the order statistics of a random sample of size n -1 from the uniform distribution U(0,1), for each n . A new integral transformation that is similar to generalized Stieltjes transform is given with various properties. Integral representation of the Gauss-hypergeometric function in some parts is employed to achieve the exact distribution. Also the result of Soltani and Roozegar [On distribution of randomly ordered uniform incremental weighted averages: Divided difference approach. Statist Probab Lett. 2012;82(5):1012-1020] with the new transform is achieved. Finally, several new examples of this family of distributions are investigated.