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Topic:
Integrals of gaussians / normal distributions
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Maxime
Posts:
1
Registered:
7/15/13


Integrals of gaussians / normal distributions
Posted:
Jul 15, 2013 9:39 PM


Hi, I'm searching for calculate some integrals with gaussians, or with normal distributions. Let's define : phi_A(x) the normal distribution with std=igma_A and mean=u_A. phi_B(x) the normal distribution with std=igma_B and mean=u_B. PHI_A(x) the cumulative of phi_A(x). PHI_B(x) the cumulative of phi_B(x).
So I want to get the mean of phi_A*PHI_B (and variance, as well). Therefore, I have to calculate this integral :
int(x*phi_A(x)*PHI_B(x),x=Inf..+Inf)
If A=B, it's trivial, and given here : http://en.wikipedia.org/wiki/List_of_integrals_of_Gaussian_functions
But as A and B are different (ie, mu_A and mu_B are different, sigma_A and sigma_B are different), it's not so easy. I tried to do it by parts, but x*Phi_B is not integrable...
Would you have any idea for getting this ? Many many thanks in advance !
Max



