Title: Product of triangular distributions with range [0, 1]

Authors: Justin R. Chimka; Raj Anand Rajagopalan

Addresses: Department of Industrial Engineering, University of Arkansas, 800 W Dickson St, Fayetteville AR 72701, USA ' Flat F-003, Gopalan Grandeur, Hoodi Circle, Bangalore, Karnataka – 560048, India

Abstract: Where random variables have unknown distributions approximated by triangular distributions, products of random variables cannot be derived, so we are left to observe random samples of such a product and hope it might be well approximated with some familiar distribution. Parameters of the beta distribution are expressed as a second-degree polynomial in c1 and c2, where c1 and c2 are the modes of triangular distributions to be multiplied. Given observations of the responses α1 and α2, and corresponding independent variables c1 and c2, we model the beta distribution parameters as multiple linear functions of their original triangular distribution parameters c1 and c2. Evidence suggests that the product of independent triangular random variables has the approximate distribution of the beta with parameters that are functions of the original triangular random variables' parameters.

Keywords: beta distribution; random variables algebra; triangular distributions; modelling.

DOI: 10.1504/IJQET.2014.064408

International Journal of Quality Engineering and Technology, 2014 Vol.4 No.3, pp.261 - 268

Received: 07 Apr 2014
Accepted: 04 May 2014

Published online: 13 Sep 2014 *

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