Gamma distribution

used:

• model the time required to service customers in queuing systems
• lifetime of devices and systems in reliability studies
• defect clustering behaviour in VLSI chips

The probability density function is given by:

$$f_X(x)=\frac{\lambda (\lambda x{)}^{\alpha -1}{e}^{-\lambda x}}{\Gamma (\alpha )}$$

where:

• $x\in (0,\infty )$. The input variable as usual.
• Two parameters $\alpha >0$ and $\lambda >0$.
• And $\Gamma (z)$ is the gamma function.