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Gaunt RE. The basic distributional theory for the product of zero mean correlated normal random variables. STAT NEERL 2022. [DOI: 10.1111/stan.12267] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
Affiliation(s)
- Robert E. Gaunt
- Department of Mathematics The University of Manchester, Oxford Road Manchester UK
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Lu D, Yang J. Identifying the distribution of linear combinations of gamma random variables via Stein’s method. COMMUN STAT-THEOR M 2021. [DOI: 10.1080/03610926.2021.1945104] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
- Dawei Lu
- School of Mathematical Sciences, Dalian University of Technology, Dalian, China
- Key Laboratory for Computational Mathematics and Data Intelligence of Liaoning Province Dalian, Dalian University of Technology, Dalian, China
| | - Jingcai Yang
- School of Mathematical Sciences, Dalian University of Technology, Dalian, China
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Approximating the Distribution of the Product of Two Normally Distributed Random Variables. Symmetry (Basel) 2020. [DOI: 10.3390/sym12081201] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
Abstract
The distribution of the product of two normally distributed random variables has been an open problem from the early years in the XXth century. First approaches tried to determinate the mathematical and statistical properties of the distribution of such a product using different types of functions. Recently, an improvement in computational techniques has performed new approaches for calculating related integrals by using numerical integration. Another approach is to adopt any other distribution to approximate the probability density function of this product. The skew-normal distribution is a generalization of the normal distribution which considers skewness making it flexible. In this work, we approximate the distribution of the product of two normally distributed random variables using a type of skew-normal distribution. The influence of the parameters of the two normal distributions on the approximation is explored. When one of the normally distributed variables has an inverse coefficient of variation greater than one, our approximation performs better than when both normally distributed variables have inverse coefficients of variation less than one. A graphical analysis visually shows the superiority of our approach in relation to other approaches proposed in the literature on the topic.
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