egpd: Expectiles of Generalized Pareto Distribution

In AntoineUC/Expectrem: Bias-reduced estimation of extreme value index and extreme quantiles, expectiles and Expected Shortfalls

Expectiles of Generalized Pareto Distribution

Description

This function computes expectiles of the Generalized Pareto Distribution.

Usage

egpd(probs, alpha, start.pt="quantile", tol=1e-08, maxiter=100, x0=NULL)

Arguments

probs	Numeric vector of probabilities with values in (0,1).
alpha	Parameter strictly greater than 1.
start.pt	Choice of the starting points. Mean of the GPD distribution if "mean", quantiles (levels probs) of the GPD distribution if "quantile". The starting point is chosen manually if "custom".
tol	Tolerance in the stopping criterion. Default: 1e-08.
maxiter	Maximum number of iterations. Default: 100.
x0	Value of the starting point (only if start.pt="custom").

Details

The considered GPD has c.s.f. (1+ y/alpha)^(-alpha). Note that the GPD is heavy-tailed with first and second order tail indices gamma=1/alpha and rho=-1/alpha, respectively.

Author(s)

Antoine Usseglio-Carleve

AntoineUC/Expectrem documentation built on Feb. 14, 2025, 11:22 a.m.