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Henry
Posts:
1,089
Registered:
12/6/04


Re: Product of two normal PDF vs 'Propogation of Uncertainty'
Posted:
Jan 21, 2011 7:40 AM


On Jan 20, 11:43 pm, Matt Francis <mattjamesfran...@gmail.com> wrote:
> To throw a different spanner in the works, I found this pagehttps://ccrma.stanford.edu/~jos/sasp/Product_Two_Gaussian_PDFs.html > which presents a closed form solution for the mean and variance of the > product of two normal distributions, which it claims is also a normal > distribution (as far as I can tell it doesn't claim that this is an > approximation). This doesn't agree with the best fit normal PDF I get > from my Monte Carlo calculation, or the simple 'error propogation' > formula??
The product of two Gaussian (probability density) functions is proprotional to a Gaussian function, as in your link above.
The product of two Gaussian distributed random variables is not Gaussian distributed. If the means are zero then the product's probability density is proportional to a modified Bessel function of the second kind. See http://mathworld.wolfram.com/NormalProductDistribution.html



