Distribution of sum of normal and gamma random variable
Let 
where )
and )
using this parametrization of the Gamma distribution. Also assume 
and 
are independent. Then what is the distribution (pdf) of 
?
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This question doesn't seem as straightforward as it sounds. For example, I have tried using the convolution formulas here, but can't seem to find a closed form expression for the integral. I have also tried multiplying the moment generating functions (mgfs) of and , but it does not seem to match up to any known mgfs.
Does anyone have any ideas on how to find the distribution for ?
Re: Distribution of sum of normal and gamma random variable
I doubt that this will get you a closed form but did you try using characteristic functions?
Re: Distribution of sum of normal and gamma random variable
Quote:
Originally Posted by
romsek 
I doubt that this will get you a closed form but did you try using characteristic functions?
I'm not too sure what characteristic functions are, how would I apply that here?
Re: Distribution of sum of normal and gamma random variable
it's basically the fourier transform of a probability distribution function and as such the characteristic function of the sum of 2 rvs is the product of the individual characteristic functions.
I just came across this
http://cran.r-project.org/web/packag...ormalGamma.pdf
it won't give you a closed form answer but it might be of interest.
