A New R-Function to Estimate the PDF of the Product of Two Uncorrelated Normal Variables

Antonio Seijas-Macias (), Amílcar Oliveira and Teresa A. Oliveira
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Antonio Seijas-Macias: Departamento de Economía, Facultade de Economía e Empresa, Universidade da Coruña, 15071 Coruña, Spain
Amílcar Oliveira: Departamento de Ciência e Tecnologia, Universidade Aberta, 1269-001 Lisboa, Portugal
Teresa A. Oliveira: CEAUL, Faculdade de Ciências, Universidade de Lisboa, 1749-016 Lisboa, Portugal

Mathematics, 2023, vol. 11, issue 16, 1-13

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 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.

Keywords: Rohatgi’s theorem; numerical integration; normal distribution; product normal variables (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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