Product of Gaussian and Rayleigh distributions gives what distribution?

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Summary:

Finding out the distribution of the product of a Gaussian and a Rayleigh distributed random variables.

Main Question or Discussion Point

Hello,

I'm trying to find out the distribution function (cumulative or density) of the product of two independent random variables respectively following a non-zero-mean Gaussian and a Rayleigh distribution. The math is too intricate for me, I've found in the appendix of [Probability Distributions Involving Gaussian Random Variables - Simon, Marvin K.] the density for the product of a zero-mean Gaussian and a Rayleigh but this will not work for what I am trying to do.


Would anyone have a reference that could help me ?
 

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