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Thread: Product of Half Normal Distributions

  1. #1
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    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?

    Thanks a lot in advance
    Regards,
    Giorgio
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  2. #2
    MHF Contributor
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    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.

    $\mu_z = \dfrac 2 \pi$

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