Certain Family of Some Beta Distributions Arising from Distribution of Randomly Weighted Average

2015/08/07 by Roozegar, Rasool
#FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1508.01731

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. 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 this new transform and also integral representation of the Gauss-hypergeometric function in some parts are employed to achieve the exact distribution. Several examples of the new family are investigated.

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