Template:Gumbel mean median and mode

The Gumbel Mean, Median and Mode

The Gumbel mean or MTTF is:

[math]\displaystyle{ \overline{T}=\mu -\sigma \gamma }[/math]

where [math]\displaystyle{ \gamma \approx 0.5772 }[/math] (Euler's constant).

The mode of the Gumbel distribution is:

[math]\displaystyle{ \tilde{T}=\mu }[/math]

The median of the Gumbel distribution is:

[math]\displaystyle{ \widehat{T}=\mu +\sigma \ln (\ln (2)) }[/math]