althill {tea}

Alternative Hill Plot

Description

Plots the Alternative Hill Plot and an averaged version of it against the upper order statistics.

Usage

althill(data, u = 2, kmin = 5, conf.int = FALSE)

Arguments

data

vector of sample data

u

gives the amount of which the Hill estimator is averaged. Default ist set to u=2.

kmin

gives the minimal k for which the graph is plotted. Default ist set to kmin=5.

conf.int

logical. If FALSE (default) no confidence intervals are plotted

Details

The Alternative Hill Plot is just a normal Hill Plot scaled to the [0,1] interval which can make interpretation much easier. See references for more information.

Value

The normal black line gives a simple Hill Plot scaled to [0,1]. The red dotted line is an averaged version that smoothes the Hill Plot by taking the mean of k(u-1) subsequent Hill estimations with respect to k. See references for more information.

References

Resnick, S. and Starica, C. (1997). Smoothing the Hill estimator. Advances in Applied Probability, 271–293.

Examples

data=rexp(500)
althill(data)