{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:27:30Z","timestamp":1760149650107,"version":"build-2065373602"},"reference-count":17,"publisher":"MDPI AG","issue":"16","license":[{"start":{"date-parts":[[2023,8,14]],"date-time":"2023-08-14T00:00:00Z","timestamp":1691971200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UIBD\/00006\/2020","C\u00e1tedra de Internacionalizaci\u00f3n Luis Fern\u00e1ndez Somoza"],"award-info":[{"award-number":["UIBD\/00006\/2020","C\u00e1tedra de Internacionalizaci\u00f3n Luis Fern\u00e1ndez Somoza"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Fundaci\u00f3n Univesidade da Coru\u00f1a","award":["UIBD\/00006\/2020","C\u00e1tedra de Internacionalizaci\u00f3n Luis Fern\u00e1ndez Somoza"],"award-info":[{"award-number":["UIBD\/00006\/2020","C\u00e1tedra de Internacionalizaci\u00f3n Luis Fern\u00e1ndez Somoza"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematics"],"abstract":"<jats:p>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\u2019s 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.<\/jats:p>","DOI":"10.3390\/math11163515","type":"journal-article","created":{"date-parts":[[2023,8,14]],"date-time":"2023-08-14T11:07:10Z","timestamp":1692011230000},"page":"3515","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A New R-Function to Estimate the PDF of the Product of Two Uncorrelated Normal Variables"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6056-3257","authenticated-orcid":false,"given":"Antonio","family":"Seijas-Macias","sequence":"first","affiliation":[{"name":"Departamento de Econom\u00eda, Facultade de Econom\u00eda e Empresa, Universidade da Coru\u00f1a, 15071 Coru\u00f1a, Spain"},{"name":"CEAUL, Faculdade de Ci\u00eancias, Universidade de Lisboa, 1749-016 Lisboa, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5500-7742","authenticated-orcid":false,"given":"Am\u00edlcar","family":"Oliveira","sequence":"additional","affiliation":[{"name":"Departamento de Ci\u00eancia e Tecnologia, Universidade Aberta, 1269-001 Lisboa, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3283-9946","authenticated-orcid":false,"given":"Teresa A.","family":"Oliveira","sequence":"additional","affiliation":[{"name":"CEAUL, Faculdade de Ci\u00eancias, Universidade de Lisboa, 1749-016 Lisboa, Portugal"},{"name":"Departamento de Ci\u00eancia e Tecnologia, Universidade Aberta, 1269-001 Lisboa, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1017\/S0305004100010690","article-title":"The distribution of second order moment statistics in a normal system","volume":"28","author":"Wishart","year":"1932","journal-title":"Math. 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Math."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2501","DOI":"10.1016\/j.spl.2009.09.004","article-title":"Product of n independent uniform random variables","volume":"79","author":"Dettmann","year":"2009","journal-title":"Stat. Probab. Lett."},{"key":"ref_17","unstructured":"R Core Team (2015). R Foundation for Statistical Computing. 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