Gamma Distribution

A distribution of independent $Exponential(\lambda )$ values.

PDF

$$f(x)=\{\begin{array}{ll}\frac{{\lambda }^a}{\Gamma (a)}{x}^{a-1}{e}^{-\lambda x}& x>0\\ 0& x\le 0\end{array}$$

• Where $a,\lambda >0$
• Where $\Gamma$ is the Gamma Function
• Denoted by $X\sim Gamma(a,\lambda )$

CDF

No closed form CDF, unless $a=1$, then this is Exponential Continuous Probability Distribution