Template:GammaDistribution

The Gamma Distribution

The gamma distribution is a flexible distribution that may offer a good fit to some sets of life data. Sometimes called the Erlang distribution, gamma distribution has applications in Bayesian analysis as a prior distribution and is also commonly used in queuing theory. The [math]\displaystyle{ pdf }[/math] of the gamma distribution is given by:

[math]\displaystyle{ \begin{align} f(t)= & \frac{e^{kz-{e^{z}}}}{t\Gamma(k)} \\ z= & \ln{t}-\mu \end{align} }[/math]

where:

[math]\displaystyle{ \begin{align} \mu = & \text{scale parameter} \\ k= & \text{shape parameter} \end{align} }[/math]

where 0 [math]\displaystyle{ \lt t\lt \infty }[/math] , [math]\displaystyle{ -\infty \lt \mu \lt \infty }[/math] and [math]\displaystyle{ k\gt 0 }[/math].

The gamma distribution and its characteristics are presented in more detail in Chapter 13.