# Thread: The product of 2 distribution

1. ## The product of 2 distribution

Hi all
Can someone teach me how to derive the normal product distribution and the noncentral rayleigh product distribution. Thanks.

2. Originally Posted by jjll
Hi all
Can someone teach me how to derive the normal product distribution and the noncentral rayleigh product distribution. Thanks.
The pdf of the product of two independent random variables X and Y with pfd f(x) and g(y) respectively is given by

$\displaystyle h(u) = \int_{-\infty}^{+\infty} \frac{1}{|y|} f\left( \frac{u}{y}\right) \, g(y) \, dy$.

The answers given to you at the other websites you have posted these questions apply here too. Getting the product of two standard normal distributions requires knowledge of the modified Bessel Function of the Second Kind. When the mean of the normal distributions is not equal to zero the question is much tougher. Why do you want to know how to get these distributions?

There have been other posts asking the same thing in this subforum. Find them and read the links that have been given.

3. Originally Posted by mr fantastic
The pdf of the product of two independent random variables X and Y with pfd f(x) and g(y) respectively is given by

$\displaystyle h(u) = \int_{-\infty}^{+\infty} \frac{1}{|y|} f\left( \frac{u}{y}\right) \, g(y) \, dy$.

The answers given to you at the other websites you have posted these questions apply here too. Getting the product of two standard normal distributions requires knowledge of the modified Bessel Function of the Second Kind. When the mean of the normal distributions is not equal to zero the question is much tougher. Why do you want to know how to get these distributions?

There have been other posts asking the same thing in this subforum. Find them and read the links that have been given.
mr fantastic, thanks for your information
I need this distribution because I am studying an algorithm of the signal process. I want to put it on that environment. So I need this information to analysis.