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Keywords = Rohatgi’s theorem

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13 pages, 318 KB  
Article
A New R-Function to Estimate the PDF of the Product of Two Uncorrelated Normal Variables
by Antonio Seijas-Macias, Amílcar Oliveira and Teresa A. Oliveira
Mathematics 2023, 11(16), 3515; https://doi.org/10.3390/math11163515 - 14 Aug 2023
Viewed by 2260
Abstract
This paper analyses the implementation of a procedure using the software R to calculate the Probability Density Function (PDF) of the product of two uncorrelated Normally Distributed Random Variables. The problem of estimating the distribution of the product of two random variables has [...] Read more.
This paper analyses the implementation of a procedure using the software R to calculate the Probability Density Function (PDF) of the product of two uncorrelated Normally Distributed Random Variables. The problem of estimating the distribution of the product of two random variables has been solved for some particular cases, but there is no unique expression for all possible situations. In our study, we chose Rohatgi’s theorem as a basis for approximating the product of two uncorrelated Normally Distributed Random Variables. The numerical approximation of the product PDF was calculated using a function that we implemented in R. Several numerical examples show that the approximations obtained in R fit the theoretical values of the product distributions. The results obtained with our R function are very positive when we compare them with the Monte Carlo Simulation of the product of the two variables. Full article
(This article belongs to the Special Issue Computational Mathematics and Numerical Analysis)
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