Hill Estimator

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Description

Hill estimator of the tail index. This estimator assumes the tail index to be positive. The threshold used is the k+1 order statistic.

Usage

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Arguments

data

vector of sample from a distribution for which the tail index is to be estimated

k

define the number of order statistics used for the estimation

Value

Hill estimator of the tail index parameter.

Author(s)

Julie Carreau

References

Embrechts, P., Kluppelberg, C. and Mikosch, T. (1997), Modelling Extremal Events, Applications of Mathematics, Stochastic Modelling and Applied Probability, Springer

See Also

gpd.mme, hpareto.mme

Examples

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r<-rhpareto(5000,0.2,-50,1,trunc=TRUE)  # tail index is equal to 0.2
 # Hill estimator of the tail index with the 100 largest observations
hillest(r,10)

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