What is the distribution of the difference of two gamma distributions with same scale parameter, and shape parameter of the first one is k(1+e), e -> 0 and second one is k.(adsbygoogle = window.adsbygoogle || []).push({});

What i exactly want to know is the following.

X~Gamma(K(1+e),\theta)

Y~Gamma(K,\theta)

Prob (X>Y) or P(X-Y)>0.

While trying to integrate i am stuck at the following intermediate step.

int (0,inf) (y)^(Ke-1) exp(-y/"\theta") Gamma(K,y/"\thata") dy.

Please suggest any way out.

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# What is the distribution of difference of two Gamma Distributions ?

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