Normal Product Distribution


The distribution of a product of two normally distributed variates X and Y with zero means and variances sigma_x^2 and sigma_y^2 is given by


where delta(x) is a delta function and K_n(z) is a modified Bessel function of the second kind. This distribution is plotted above in red.

The analogous expression for a product of three normal variates can be given in terms of Meijer G-functions as


plotted above in blue.

See also

Normal Difference Distribution, Normal Distribution, Normal Ratio Distribution, Normal Sum Distribution

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Cite this as:

Weisstein, Eric W. "Normal Product Distribution." From MathWorld--A Wolfram Web Resource.

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