Anderson-Darling goodness-of-fit test for a fitted GEV

The A^2 statistic is Anderson and Darling (1952), read from the corpus PDF as Hedderich, Sachs and Reynarowych eq (7.33); the single implementation lives in Adcore and is called, not copied. The probability-integral transform is the generalized extreme value distribution function, Coles (2001), An Introduction to Statistical Modeling of Extreme Values, eq (3.2): G(z) = exp(-(1 + xi (z-mu)/sigma)^(-1/xi)) on 1 + xi (z-mu)/sigma > 0, and G(z) = exp(-exp(-(z-mu)/sigma)) when xi = 0.

Usage

Adgev(x, mu = 0, sigma = 1, xi = 0)

Arguments

x

Numeric block maxima.

mu, sigma, xi

Location, scale and shape. Supplied, not fitted.

Value

list: statistic, u, mu, sigma, xi, n, method.

Details

Parameters are supplied by the caller, not fitted. That is deliberate: the package GEV/GPD fitters are Nelder-Mead and agree across language arms only to about 1e-4, which would make the statistic irreproducible. No p-value is returned: Stephens (1986) critical values depend on which parameters were estimated and how, and that chapter was not obtainable here.

Examples

Adgev(c(0.1, 0.9, 1.4, 2.2, 3.1), 1, 1, 0.1)$statistic
#> [1] 0.1581766