POT: gpd2frech – R documentation

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gpd2frech

Transforms GPD Observations to Unit Frechet Ones and Vice Versa

Transforms GPD observations to unit Frechet ones and vice versa

gpd2frech(x, loc = 0, scale = 1, shape = 0, pat = 1)
frech2gpd(z, loc = 0, scale = 1, shape = 0, pat = 1)

`x,z`	The vector of observations.
`loc,scale,shape`	The location, scale and shape parameters respectively.
`pat`	The proportion above the threshold, i.e. Pr[X > log] = pat.

Let x_i, i=1,…,n be the realisation of a GPD random variable. Thus, the transformation to unit Frechet is defined as:

z_i = -1 / log [1 - pat (1 + shape *(x_i - loc) / scale)_+^(-1/shape)]

A numeric vector.

Mathieu Ribatet

x <- rgpd(10, 0, 1, 0.25)
z <- gpd2frech(x, 0, 1, 0.25)
z
all(frech2gpd(z, 0, 1, 0.25) == x)

Generalized Pareto Distribution and Peaks Over Threshold

v1.1-10

GPL (>= 2)

Authors

Mathieu Ribatet [aut], Christophe Dutang [ctb,cre]

Initial release