Mixing
Solving definite integral over product of normal pdf and cdf
$begingroup$
I'm looking for a solution to the following integral (not sure if one exists)
$$ int_0^infty phi(x,mu_1,sigma_1)Phi (x,mu_2,sigma_2) mathrm{d}x,$$
where $phi(x,mu_1,sigma_1)$ denotes a normal PDF with mean $mu_1$ and standard deviation $sigma_1$ and $Phi (x,mu_2,sigma_2)$ denotes a normal CDF with mean $mu_2$ and standard deviation $sigma_2$, respectively.
Some related results are available (https://en.wikipedia.org/wiki/List_of_integrals_of_Gaussian_functions), but I'm not sure how to generalize them to the case of non-zero mean values.
integration normal-distribution
asked Feb 1 at 19:38
EnzoEnzo
424
$endgroup$
add a comment |
$begingroup$
I'm looking for a solution to the following integral (not sure if one exists)
$$ int_0^infty phi(x,mu_1,sigma_1)Phi (x,mu_2,sigma_2) mathrm{d}x,$$
where $phi(x,mu_1,sigma_1)$ denotes a normal PDF with mean $mu_1$ and standard deviation $sigma_1$ and $Phi (x,mu_2,sigma_2)$ denotes a normal CDF with mean $mu_2$ and standard deviation $sigma_2$, respectively.
Some related results are available (https://en.wikipedia.org/wiki/List_of_integrals_of_Gaussian_functions), but I'm not sure how to generalize them to the case of non-zero mean values.
integration normal-distribution
asked Feb 1 at 19:38
EnzoEnzo
424
$endgroup$
add a comment |
$begingroup$
I'm looking for a solution to the following integral (not sure if one exists)
$$ int_0^infty phi(x,mu_1,sigma_1)Phi (x,mu_2,sigma_2) mathrm{d}x,$$
where $phi(x,mu_1,sigma_1)$ denotes a normal PDF with mean $mu_1$ and standard deviation $sigma_1$ and $Phi (x,mu_2,sigma_2)$ denotes a normal CDF with mean $mu_2$ and standard deviation $sigma_2$, respectively.
Some related results are available (https://en.wikipedia.org/wiki/List_of_integrals_of_Gaussian_functions), but I'm not sure how to generalize them to the case of non-zero mean values.
integration normal-distribution
asked Feb 1 at 19:38
EnzoEnzo
424
$endgroup$
I'm looking for a solution to the following integral (not sure if one exists)
$$ int_0^infty phi(x,mu_1,sigma_1)Phi (x,mu_2,sigma_2) mathrm{d}x,$$
where $phi(x,mu_1,sigma_1)$ denotes a normal PDF with mean $mu_1$ and standard deviation $sigma_1$ and $Phi (x,mu_2,sigma_2)$ denotes a normal CDF with mean $mu_2$ and standard deviation $sigma_2$, respectively.
Some related results are available (https://en.wikipedia.org/wiki/List_of_integrals_of_Gaussian_functions), but I'm not sure how to generalize them to the case of non-zero mean values.
integration normal-distribution
integration normal-distribution
asked Feb 1 at 19:38
EnzoEnzo
424
asked Feb 1 at 19:38
EnzoEnzo
424
asked Feb 1 at 19:38
EnzoEnzo
424
asked Feb 1 at 19:38
EnzoEnzo
424
asked Feb 1 at 19:38
EnzoEnzo
424
424
add a comment |
add a comment |
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