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

Same A^2 statistic as Adgev, computed by Adcore, which holds the single implementation (Hedderich, Sachs and Reynarowych eq (7.33); Anderson and Darling 1952). Only the probability-integral transform changes: here it is the generalized Pareto distribution function, Coles (2001) eq (4.2), H(y) = 1 - (1 + xi y/sigma)^(-1/xi) for y > 0, and H(y) = 1 - exp(-y/sigma) when xi = 0.

Usage

Adgpd(y, sigma = 1, xi = 0)

Arguments

y

Numeric threshold excesses, all positive.

sigma, xi

Scale and shape. Supplied, not fitted.

Value

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

Details

y are threshold excesses and must be positive; the caller subtracts the threshold. Parameters are supplied, not fitted, for the same reproducibility reason as Adgev. No p-value is returned.

Examples

Adgpd(c(0.2, 0.7, 1.3, 2.0, 3.4), 1, 0.1)$statistic
#> [1] 0.6691444