Exact Distribution of Random Weighted Convolution of Some Beta Distributions Through an Integral Transform, By Abouzar Bazyari

Research

Title	Exact Distribution of Random Weighted Convolution of Some Beta Distributions Through an Integral Transform
Type	Article
Keywords	—
Journal	Pakistan Journal of Statistics and Operation Research
DOI	—
Researchers	Rasool Roozegar (First researcher) , Abouzar Bazyari (Second researcher)

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.