extremefit (version 1.0.2)

hill: Hill estimator

Description

Compute the weighted Hill estimator.

Usage

hill(X, weights = rep(1, length(X)), grid = X)

Value

xsort

the sorted data.

wsort

the weights assiociated to \(xsort\).

grid

the grid for which the Hill estimator is computed.

hill

the Hill estimators.

Arguments

X

a vector of data.

weights

a vector of weights assiociated to \(x\).

grid

a vector of values for which the Hill estimator is computed.

Author

Ion Grama

Details

Compute the weighted Hill estimator for vectors \(grid\), data and weights (see references below).

References

Grama, I. and Spokoiny, V. (2008). Statistics of extremes by oracle estimation. Ann. of Statist., 36, 1619-1648.

Durrieu, G. and Grama, I. and Pham, Q. and Tricot, J.- M (2015). Nonparametric adaptive estimator of extreme conditional tail probabilities quantiles. Extremes, 18, 437-478.

Hill, B.M. (1975). A simple general approach to inference about the tail of a distribution. Annals of Statistics, 3, 1163-1174.

Examples

X <- abs(rcauchy(100))
weights <- rep(1, length(X))
wh <- hill(X, w = weights)