GEV |
$\frac{1}{\alpha }{{\left[ 1\text{- }\!\!\beta\!\!\text{ }\left( \frac{v-\mu }{\alpha } \right) \right]}^{{1}/{\text{ }\!\!\beta\!\!\text{ -1}}\;}}\exp \left\{ \text{-}{{\left[ 1\text{- }\!\!\beta\!\!\text{ }\left( \frac{v-\mu }{\alpha } \right) \right]}^{{1}/{\text{ }\!\!\beta\!\!\text{ }}\;}} \right\}$ |
μ-location parameter α-scale parameter β-shape parameter |
Gumbel |
$\frac{1}{\text{ }\!\!\alpha\!\!\text{ }}\overset{\text{ }\!\!\mu\!\!\text{ }}{\mathop{\exp }}\,\left[ -\left( \frac{v-}{\text{ }\!\!\alpha\!\!\text{ }} \right)\overset{\text{ }\!\!\mu\!\!\text{ }}{\mathop{-\exp }}\,\left( -\frac{v-}{\text{ }\!\!\alpha\!\!\text{ }} \right) \right]$ |
μ-location parameter α-scale parameter |
Weibull |
$\frac{\text{ }\!\!\alpha\!\!\text{ }}{\text{ }\!\!\beta\!\!\text{ }}{{\left( v-\text{ }\!\!\mu\!\!\text{ } \right)}^{\text{ }\!\!\alpha\!\!\text{ }-1}}\exp \left[ -\frac{{{\left( v-\text{ }\!\!\mu\!\!\text{ } \right)}^{\text{ }\!\!\alpha\!\!\text{ }}}}{\text{ }\!\!\beta\!\!\text{ }} \right]\,\,\,\,\,\,\,\,\,\,\,\,\,\,x\ge \text{ }\!\!\mu\!\!\text{ }$ |
μ-location parameter β-shape parameter α-scale parameter |
P-III |
$\frac{{{\text{ }\!\!\beta\!\!\text{ }}^{\text{ }\!\!\alpha\!\!\text{ }}}}{\Gamma \left( \text{ }\!\!\alpha\!\!\text{ } \right)}{{\left( v\,\text{- }\!\!\mu\!\!\text{ } \right)}^{\text{ }\!\!\alpha\!\!\text{ -1}}}{{e}^{\text{- }\!\!\beta\!\!\text{ }\left( x-\text{ }\!\!\mu\!\!\text{ } \right)}}\,\,\,{{v}^{3}}\text{ }\!\!\mu\!\!\text{ , }\!\!\alpha\!\!\text{ }\,\text{}\,\text{0}$ |
μ-location parameter β-shape parameter α-scale parameter |