Distributions#

Generalized extreme value distribution (GEV)#

  • The generalised extreme value (or generalized extreme value) distribution characterises the behaviour of ‘block

    maxima’

probability density function (pdf)#

f(x) = \frac{1}{\sigma}\ast{Q(x)}^{\xi+1}\ast e^{-Q(x)}

  • where
    • math

      sigma is the scale parameter

    • math

      mu is the location parameter

    • math

      delta is the scale parameter

Cumulative distribution function (cdf)#

F(x)=e^{-Q(x)}

Gumbel Distribution#

probability density function (pdf)#

f(x) = \frac{1}{\sigma} \ast { {e}^{-(\frac{x-\mu}{\delta}) - {e}^{- (\frac{x-\mu}{\delta})} }}

Cumulative distribution function (cdf)#

F(x) = {e}^{- {e}^{- (\frac{x-\mu}{\delta})} }