Evaluation of kurtosis into the product of two normally distributed variables

Oliveira, Amilcar; Seijas-Macias, J. Antonio; Oliveira, Teresa A.

http://hdl.handle.net/10400.2/14687

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Autores

Oliveira, Amilcar

Seijas-Macias, J. Antonio

Oliveira, Teresa A.

Resumo(s)

Kurtosis (k) 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 (k = 3), independently of the value of the two parameters: mean and variance. In fact, the excess kurtosis is defined as k - 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.