Product of triangular distributions with range [0, 1]
by Justin R. Chimka; Raj Anand Rajagopalan
International Journal of Quality Engineering and Technology (IJQET), Vol. 4, No. 3, 2014

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.

Online publication date: Sat, 13-Sep-2014

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