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

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  • Antonio Seijas-Macias

    (Departamento de Economía, Facultade de Economía e Empresa, Universidade da Coruña, 15071 Coruña, Spain
    CEAUL, Faculdade de Ciências, Universidade de Lisboa, 1749-016 Lisboa, Portugal
    These authors contributed equally to this work.)

  • Amílcar Oliveira

    (Departamento de Ciência e Tecnologia, Universidade Aberta, 1269-001 Lisboa, Portugal
    These authors contributed equally to this work.)

  • Teresa A. Oliveira

    (CEAUL, Faculdade de Ciências, Universidade de Lisboa, 1749-016 Lisboa, Portugal
    Departamento de Ciência e Tecnologia, Universidade Aberta, 1269-001 Lisboa, Portugal
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Antonio Seijas-Macias & Amílcar Oliveira & Teresa A. Oliveira, 2023. "A New R-Function to Estimate the PDF of the Product of Two Uncorrelated Normal Variables," Mathematics, MDPI, vol. 11(16), pages 1-13, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:16:p:3515-:d:1217218
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    References listed on IDEAS

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    1. Robert E. Gaunt, 2022. "The basic distributional theory for the product of zero mean correlated normal random variables," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 76(4), pages 450-470, November.
    2. Dettmann, Carl P. & Georgiou, Orestis, 2009. "Product of n independent uniform random variables," Statistics & Probability Letters, Elsevier, vol. 79(24), pages 2501-2503, December.
    3. Glen, Andrew G. & Leemis, Lawrence M. & Drew, John H., 2004. "Computing the distribution of the product of two continuous random variables," Computational Statistics & Data Analysis, Elsevier, vol. 44(3), pages 451-464, January.
    4. Robert E. Gaunt, 2019. "A note on the distribution of the product of zero‐mean correlated normal random variables," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 73(2), pages 176-179, May.
    5. Robert E. Gaunt, 2021. "Stein’s method and the distribution of the product of zero mean correlated normal random variables," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 50(2), pages 280-285, January.
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