Template:Gumbel probability density function

Gumbel Probability Density Function

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

[math]\displaystyle{ f(T)=\frac{1}{\sigma }{{e}^{z-{{e}^{z}}}} }[/math]

[math]\displaystyle{ f(T)\ge 0,\sigma \gt 0 }[/math]

where:

[math]\displaystyle{ z=\frac{T-\mu }{\sigma } }[/math]

and:

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