Institute of Mathematical Statistics Lecture Notes - Monograph Series

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

T. S. T. Wong and W. K. Li

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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

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

First available in Project Euclid: 28 November 2007

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

generalized extreme value distribution generalized Pareto distribution maximum product of spacings maximum likelihood Moran's statistic

Copyright © 2006, Institute of Mathematical Statistics


Wong, T. S. T.; Li, W. K. A note on the estimation of extreme value distributions using maximum product of spacings. Time Series and Related Topics, 272--283, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2006. doi:10.1214/074921706000001102.

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