## Institute of Mathematical Statistics Lecture Notes - Monograph Series

### A note on the estimation of extreme value distributions using maximum product of spacings

#### Abstract

The maximum product of spacings (MPS) is employed in the estimation of the Generalized Extreme Value Distribution (GEV) and the Generalized Pareto Distribution (GPD). Efficient estimators are obtained by the MPS for all $\gamma$. This outperforms the maximum likelihood method which is only valid for $\gamma< 1$. It is then shown that the MPS gives estimators closer to the true parameters compared to the maximum likelihood estimates (MLE) in a simulation study. In cases where sample sizes are small, the MPS performs stably while the MLE does not. The performance of MPS estimators is also more stable than those of the probability-weighted moment (PWM) estimators. Finally, as a by-product of the MPS, a goodness of fit statistic, Moran's statistic, is available for the extreme value distributions. Empirical significance levels of Moran's statistic calculated are found to be satisfactory with the desired level.

#### Chapter information

Source
Hwai-Chung Ho, Ching-Kang Ing, Tze Leung Lai, eds., Time Series and Related Topics: In Memory of Ching-Zong Wei (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2006), 272-283

Dates
First available in Project Euclid: 28 November 2007