Template:Gamma mean median and mode

The Gamma Mean, Median and Mode

The gamma mean or MTTF is:

[math]\displaystyle{ \overline{T}=k{{e}^{\mu }} }[/math]

The mode exists if [math]\displaystyle{ k\gt 1 }[/math] and is given by:

[math]\displaystyle{ \tilde{T}=(k-1){{e}^{\mu }} }[/math]

The median is:

[math]\displaystyle{ \widehat{T}={{e}^{\mu +\ln (\Gamma _{I}^{-1}(0.5;k))}} }[/math]