einvgamma: Expectiles of Inverse-Gamma distribution

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

Expectiles of Inverse-Gamma distribution

Description

This function computes the expectiles of the Inverse-Gamma distribution.

Usage

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

Arguments

probs	Numeric vector of probabilities with values in (0,1).
alpha	Shape parameter strictly greater than 1.
lambda	Scale parameter strictly greater than 0.
start.pt	Choice of the starting points. Mean of the Inverse-Gamma distribution if "mean", quantiles (levels probs) of the Inverse-Gamma 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 distribution has p.d.f. lambda^alpha*y^(-alpha-1)*exp(-lambda/y)/Gamma(alpha) for y>0.

Author(s)

Antoine Usseglio-Carleve

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