Fixed Point Iteration for Estimating the Parameters of Extreme Value Distributions

Abstract

Maximum likelihood estimations for the parameters of extreme value distributions are discussed in this article 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 article.

Keywords:

• Estimation
• Extreme value distributions
• Fixed point iteration
• Censored data

Mathematics Subject Classification:

• 62F10
• 62N02