Template:Gamma probability density function

Gamma Probability Density Function

The [math]\displaystyle{ pdf }[/math] of the gamma distribution is given by:

[math]\displaystyle{ f(t)=\frac{{{e}^{kz-{{e}^{z}}}}}{t\Gamma (k)} }[/math]

where:

[math]\displaystyle{ z=\ln (t)-\mu }[/math]

and:

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

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