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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 dierence 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.

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How to Cite
Roozegar, R., & Bazyari, A. (2017). Exact Distribution of Random Weighted Convolution of Some Beta Distributions Through an Integral Transform. Pakistan Journal of Statistics and Operation Research, 13(4), 799-808.