Evaluation of Kurtosis into the product of two normally distributed variables

Kurtosis (κ) is any measure of the “peakedness” of a distribution of a real-valued random variable. We study the evolution of the Kurtosis for the product of two normally distributed variables. Product of two normal variables is a very common problem for some areas of study, like, physics, economics...

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Bibliographic Details
Main Authors: Oliveira, Amílcar, Oliveira, Teresa, Seijas-Macías, Antonio
Format: Conference Proceeding
Language:English
Subjects:
Independent variables
Kurtosis
Mathematical analysis
Normal distribution
Parameters
Psychology
Random variables
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Summary:Kurtosis (κ) is any measure of the “peakedness” of a distribution of a real-valued random variable. We study the evolution of the Kurtosis for the product of two normally distributed variables. Product of two normal variables is a very common problem for some areas of study, like, physics, economics, psychology, … Normal variables have a constant value for kurtosis (κ = 3), independently of the value of the two parameters: mean and variance. In fact, the excess kurtosis is defined as κ− 3 and the Normal Distribution Kurtosis is zero. The product of two normally distributed variables is a function of the parameters of the two variables and the correlation between then, and the range for kurtosis is in [0, 6] for independent variables and in [0, 12] when correlation between then is allowed.
ISSN:0094-243X
1551-7616
DOI:10.1063/1.4952232