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- Title
Exact Distribution of Random Weighted Convolution of Some Beta Distributions Through an Integral Transform.
- Authors
Roozegar, Rasool; Bazyari, Abouzar
- 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.
- Subjects
WEIGHTED graphs; MATHEMATICAL convolutions; BETA distribution; INTEGRAL transforms; STIELTJES transform
- Publication
Pakistan Journal of Statistics & Operation Research, 2017, Vol 13, Issue 4, p799
- ISSN
1816-2711
- Publication type
Article
- DOI
10.18187/pjsor.v13i4.1868