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This is the second part of a paper which focuses on reviewing methods for estimating the parameters of the generalized Pareto distribution (GPD). The GPD is a very important distribution in the extreme value context. It is commonly used for modeling the observations that exceed very high thresholds. The ultimate success of the GPD in applications evidently depends on the parameter estimation process. Quite a few methods exist in the literature for estimating the GPD parameters. Estimation procedures, such as the maximum likelihood (ML), the method of moments (MOM) and the probability weighted moments (PWM) method were described in Part I of the paper. We shall continue to review methods for estimating the GPD parameters, in particular methods that are robust and procedures that use the Bayesian methodology. As in Part I, we shall focus on those that are relatively simple and straightforward to be applied to real world data.

In Portugal, due to the combination of climatological and ecological factors, large wildfires are a constant threat and due to their economic impact, a big policy issue. In order to organize efficient fire fighting capacity and resource management, correct quantification of the risk of large wildfires are needed. In this paper, we quantify the regional risk of large wildfire sizes, by fitting a Generalized Pareto distribution to excesses over a suitably chosen high threshold. Spatio-temporal variations are introduced into the model through model parameters with suitably chosen link functions. The inference on these models are carried using Bayesian Hierarchical Models and Markov chain Monte Carlo methods.

Spatial and temporal patterns of large fire (>100 ha) incidence in Portugal over the period 1984–2004 were modeled using extreme value statistics, namely the Peaks Over Threshold approach, which uses the Generalized Pareto Distribution (GPD) as a model. The original dataset includes all fires larger than 5 ha (30 616 fires) that were observed in Portugal during the study period, mapped from Landsat satellite imagery. The country was divided into eight regions, considered internally homogeneous from the perspective of their fire regimes and respective environmental correlates. The temporal analysis showed that there does not appear to be any trend in the incidence of very large fires, but revealed a cyclical behavior in the values of the GPD shape parameter, with a period in the range of 3 to 5 years. Spatial analysis highlighted strong regional differences in the incidence of large fires, and allowed the calculation of return levels for a range of fire sizes. This analysis was affected by the presence of a few outlying observations, which may correspond to clusters of contiguous fire scars, resulting in artificially large burned areas. We discuss some of the implications of our findings in terms of consequences for fire management aimed at preventing the occurrence of extremely large fires, and present ideas for extending the present study.

Elemental percentile method, Gibbs sampling, generalized Pareto distribution, maximum likelihood, peaks over threshold, probability-weighted moments, 62F15, 62G32,