Moment Estimator for the Generalized and the Hybrid Pareto Distribution

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Description

Moment estimators for the generalized Pareto distribution and parameter estimators based on two quantiles plus a tail index estimator for the hybrid Pareto distribution.

Usage

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gpd.mme(x)
hpareto.mme(x, xi0=c(),p=0.99)

Arguments

x

vector of sample for which the parameters will be estimated

xi0

an optional a priori value for the tail index parameter

p

the percentage of largest observations used for tail index estimation

Details

For hpareto.mme, the tail index is assumed to be positive. In case one has some prior information on the value of the tail index parameter, it is possible to provide this value as an argument to the function hpareto.mme. The two other parameters mu and sigma will be estimated based on that tail index estimate and two quantiles of the hybrid Pareto distribution. If the tail index parameter is not provided as input, it will be estimated with the Hill estimator using data above the p-quantile. By default, p=0.99 but this might be inappropriate depending on the sample. Since the tail index estimate is very sensitive, it is recommended to tune carefully the p argument.

Value

A vector of parameter estimates.

Author(s)

Julie Carreau

References

Hosking, J. R. M. and Wallis, J. R. (1987), Parameter and quantile estimation for the Generalized Pareto distribution, 29, Technometrics Carreau, J. and Bengio, Y. (2009), A Hybrid Pareto Model for Asymmetric Fat-tailed Data: the Univariate Case, 12, Extremes

Examples

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r<-rhpareto(1000,0.1,0,1,trunc=FALSE)
hpareto.mme(r,p=0.991)

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