Fixed Point Iteration for Estimating The Parameters of Extreme Value Distributions

TL;DR

This paper introduces a fixed point iteration method for estimating parameters of extreme value distributions, offering a simpler alternative to Newton-Raphson and graphical methods, with theoretical validation.

Contribution

It proposes a novel fixed point iteration approach for maximum likelihood estimation of extreme value distribution parameters, simplifying implementation and unifying existing methods.

Findings

Fixed point iteration converges for parameter estimation.

The method simplifies and unifies existing approaches.

The approach is theoretically validated.

Abstract

Maximum likelihood estimations for the parameters of extreme value distributions are discussed in this paper using fixed point iteration. The commonly used numerical approach for addressing this problem is the Newton-Raphson approach which requires differentiation unlike the fixed point iteration which is also easier to implement. Graphical approaches are also usually proposed in the literature. We prove that these reduce in fact to the fixed point solution proposed in this paper.