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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