Normal Product Distribution
GaussianProductDistribution
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
| P_(XYZ)(u)=1/(2sqrt(2)pi^(3/2)sigma_xsigma_ysigma_z)G_(0,3)^(3,0)((u^2)/(8sigma_x^2sigma_y^2sigma_z^2)|0,0,0), |
(3)
|
plotted above in blue.
See also
Normal Difference Distribution, Normal Distribution, Normal Ratio Distribution, Normal Sum DistributionExplore with Wolfram|Alpha
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Cite this as:
Weisstein, Eric W. "Normal Product Distribution." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/NormalProductDistribution.html