pickands
(Package: smoothtail) :
Compute original and smoothed version of Pickands' estimator
Given an ordered sample of either exceedances or upper order statistics which is to be modeled using a GPD, this function provides Pickands' estimator of the shape parameter γ in [-1,0]. Precisely, for k=4, …, n
gpd
(Package: smoothtail) :
The Generalized Pareto Distribution
Density function, distribution function, quantile function and random generation for the generalized Pareto distribution (GPD) with shape parameter γ and scale parameter σ.
Given an ordered sample of either exceedances or upper order statistics which is to be modeled using a GPD with distribution function F, this function provides Segers' estimator of the shape parameter γ, see Segers (2005). Precisely, for k = {1, …, n-1}, the estimator can be written as
falkMVUE
(Package: smoothtail) :
Compute original and smoothed version of Falk's estimator for a known endpoint
Given an ordered sample of either exceedances or upper order statistics which is to be modeled using a GPD with distribution function F, this function provides Falk's estimator of the shape parameter γ in [-1,0] if the endpoint
Given independent and identically distributed observations X_1 < … < X_n from a Generalized Pareto distribution with shape parameter γ in [-1,0], offers three methods to compute estimates of γ. The estimates are based on the principle of replacing the order statistics X_{(1)}, …, X_{(n)} of the sample by quantiles hat X_{(1)}, …, hat X_{(n)} of the distribution function hat F_n based on the log–concave density estimator hat f_n. This procedure is justified by the fact that the GPD density is log–concave for γ in [-1,0].
● Data Source:
CranContrib
● Keywords: distribution, htest, nonparametric
● Alias: logcon, logcondens, smoothtail, smoothtail-package, tail index
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falk
(Package: smoothtail) :
Compute original and smoothed version of Falk's estimator
Given an ordered sample of either exceedances or upper order statistics which is to be modeled using a GPD, this function provides Falk's estimator of the shape parameter γ in [-1,0]. Precisely,
providing 
.