Approximating the Distribution of the Product of Two Normally Distributed Random Variables

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- Investigación (FEE) [893]
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Approximating the Distribution of the Product of Two Normally Distributed Random VariablesDate
2020Citation
Seijas-Macías, J.A., Oliveira, A., Oliveira T.A. y & Leiva.V. (2020). Approximating the Distribution of the Product of Two Normally Distributed Random Variables. Symmetry, 12, 8 (1201), pp. 1-13. https://doi.org/10.3390/SYM12081201
Abstract
[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.
Keywords
Extended skew-normal distribution
Kurtosis
Moments
R software
Skewness
Kurtosis
Moments
R software
Skewness
Editor version
Rights
Atribución 4.0 Internacional
ISSN
2073-8994