Fréchet distribution
The Fréchet distribution is a continuous distribution on the positive real numbers, which uses a real positive real scaling parameter. It is named after the French mathematician Maurice René Fréchet.
Distribution and density functions
The Fréchet distribution has a real parameter > 0, the distribution function
The corresponding density function is
Moments and median
Below is a Fréchet - distributed random variable and the gamma function.
Median
The median is
Existence of moments
The k-th moments of the Fréchet distribution exactly exist if > k
Expected value
The expectation value
Variance
The variance is
Skew
The skewness is
Kurtosis
The kurtosis is
Connection with other distributions
Is Fréchet distribution with parameters, so is Gumbel distributed with parameters and.
According to the theorem of Fisher - Tippet can converge a standardized, non- degenerate extreme value distribution only against one of three generalized extreme value distribution ( GEV), one of which is the Fréchet distribution.