What is frechet distribution?

The Fréchet distribution, also known as the double exponential distribution, is a class of extreme value distributions used in the fields of statistics and probability theory. It is named after Russian mathematician Maurice Fréchet.

The Fréchet distribution is typically used to model extreme events, such as floods, hurricanes, earthquakes, and other natural disasters. It is characterized by its heavy right tail, which indicates that extreme values are more likely to occur than in other types of distributions.

The probability density function (PDF) of the Fréchet distribution is given by:

f(x;α,β,s) = (β/s) * (x/s)^(α-1) * exp(-(x/s)^α), for x ≥ 0

where α, β, and s are the shape, scale, and location parameters, respectively. The shape parameter α determines the tail behavior of the distribution, with higher values leading to heavier tails.

The cumulative distribution function (CDF) of the Fréchet distribution is:

F(x;α,β,s) = exp(-(x/s)^α)

The Fréchet distribution is a special case of the generalized extreme value (GEV) distribution, which encompasses three distribution types: the Gumbel, Frechet, and Weibull distributions. The Fréchet distribution corresponds to the case where α > 0, with α = 1 representing the Weibull distribution and α < 0 representing the Gumbel distribution.