Gamma Distribution

The Gamma distribution is a generalization of the Exponential Distribution. While an Exponential r.v. represents the waiting time for the first success under conditions of memoryless-ness, we shall see that Gamma r.v. represents the total waiting time for multiple successes

An r.v. $Y$ is said to have the Gamma Distribution with parameters $a$ and $\lambda$, where $a>0$ and $\lambda >0$, if its PDF is

$$f(y)=\frac{1}{\Gamma (a)}(\lambda y{)}^a{e}^{-\lambda y}\frac{1}{y},y>0$$

where $\Gamma (\cdot )$ is the Gamma Function. And we write $Y\sim \mathrm{Gamma}(a,\lambda )$