Hi there,

After some algebra on a problem I have I derived the following distribution concering let's say the r.v. X.

s^(-1)*g*φ((x-g^(-1)*a)/(s*g^(-1))) *(1/ Φ(a/s)) (1).

where Φ is the cumulative normal and 1/k*φ((x-m)/k)=1/sqrt(2*π)*exp(-(x-m)^2/2*k^2), i.e. the normal density.

My question is :

Is the density in (1) some known distribution? I thought that it was a truncated normal distribution, but I am having second thoughts. I checked the wiki and the pdf of the truncated normal does not seem to match, is it? What would the mean and variance be?

Thanx in advance for any answers!!

I also have this form if it makes things easier..:

1/(s/b) φ( (x- (a/b^2)) /(s/b1) ) * ( 1/ Φ(a/(b*s) ) )

After some algebra on a problem I have I derived the following distribution concering let's say the r.v. X.

s^(-1)*g*φ((x-g^(-1)*a)/(s*g^(-1))) *(1/ Φ(a/s)) (1).

where Φ is the cumulative normal and 1/k*φ((x-m)/k)=1/sqrt(2*π)*exp(-(x-m)^2/2*k^2), i.e. the normal density.

My question is :

Is the density in (1) some known distribution? I thought that it was a truncated normal distribution, but I am having second thoughts. I checked the wiki and the pdf of the truncated normal does not seem to match, is it? What would the mean and variance be?

Thanx in advance for any answers!!

I also have this form if it makes things easier..:

1/(s/b) φ( (x- (a/b^2)) /(s/b1) ) * ( 1/ Φ(a/(b*s) ) )

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