hill: Hill estimator

In extremefit: Estimation of Extreme Conditional Quantiles and Probabilities

Hill estimator

Description

Compute the weighted Hill estimator.

Usage

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

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.

Details

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

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.

Author(s)

Ion Grama

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)

extremefit documentation built on Aug. 21, 2025, 6:03 p.m.