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

03/2007; DOI: 10.1214/074921706000001102
Source: arXiv

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.

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##### Article: A software review for extreme value analysis
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ABSTRACT: Extreme value methodology is being increasingly used by practitioners from a wide range of fields. The importance of accurately modeling extreme events has intensified, particularly in environmental science where such events can be seen as a barometer for climate change. These analyses require tools that must be simple to use, but must also implement complex statistical models and produce resulting inferences. This document presents a review of the software that is currently available to scientists for the statistical modeling of extreme events. We discuss all software known to the authors, both proprietary and open source, targeting different data types and application areas. It is our intention that this article will simplify the process of understanding the available software, and will help promote the methodology to an expansive set of scientific disciplines.
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