# Thread: Product of Half Normal Distributions

1. ## Product of Half Normal Distributions

Hello,
I have to multiply elements taken from a half normal distributions (HND).
How can I calculate the mean and variance of the result starting from the mean/variance of the HND?

Regards,
Giorgio

2. ## Re: Product of Half Normal Distributions

it looks like if $X,Y$ are both distributed as half Normal(0,1) then their product is distributed as

$Z=XY$

$f_Z(z)=\dfrac 2 \pi K_0(z),~0 \leq z$

where $K_0(z)$ is the zeroth order modified Bessel function.

$\mu_z = \dfrac 2 \pi$

$\sigma_Z = \sqrt{1-\left(\dfrac 2 \pi\right)^2}$