Parameter estimation of the generalized Pareto distribution—Part II

Bermudez, P. de Zea; Kotz, Samuel

doi:10.1016/j.jspi.2008.11.020

Cited by 70 publications

(26 citation statements)

References 35 publications

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“…The POT approach uses the GP distribution as a model to assign probabilities to the exceedances of E over a predefined threshold, i.e. to values E = E − E min (with E > E min ), where E min is a prescribed minimum value (de Zea Bermudez and Kotz, 2010). The GP cumulative distribution function of exceedances E is…”

Section: Statistical Models Of Exceedance Of Energy Released By Firesmentioning

confidence: 99%

“…Several approaches have been proposed involving different techniques to rate indices of fire danger against fire history over a given period and study area. Examples of such techniques include logistic regression and percentile analysis (Andrews et al, 2003), cluster analysis (Dymond et al, 2005) and threshold setting based on a geometric progression (Van Wagner, 1987) or on values of probability (DaCamara et al, 2014). Fire history traditionally consists of ground observations of fire occurrence (Anderson and Englefield, 2001), fire load (Merrill and Alexander, 1987), suppression difficulty (Kiil et al, 1977) and area burned (San-Miguel-Ayanz et al, 2012).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Fire danger rating over Mediterranean Europe based on fire radiative power derived from Meteosat

Pinto

DaCamara

Trigo

et al. 2018

Nat. Hazards Earth Syst. Sci.

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Abstract. We present a procedure that allows the operational generation of daily forecasts of fire danger over Mediterranean Europe. The procedure combines historical information about radiative energy released by fire events with daily meteorological forecasts, as provided by the Satellite Application Facility for Land Surface Analysis (LSA SAF) and the European Centre for Medium-Range Weather Forecasts (ECMWF). Fire danger is estimated based on daily probabilities of exceedance of daily energy released by fires occurring at the pixel level. Daily probability considers meteorological factors by means of the Canadian Fire Weather Index (FWI) and is estimated using a daily model based on a generalized Pareto distribution. Five classes of fire danger are then associated with daily probability estimated by the daily model. The model is calibrated using 13 years of data (2004–2016) and validated against the period of January–September 2017. Results obtained show that about 72 % of events releasing daily energy above 10 000 GJ belong to the “extreme” class of fire danger, a considerably high fraction that is more than 1.5 times the values obtained when using the currently operational Fire Danger Forecast module of the European Forest Fire Information System (EFFIS) or the Fire Risk Map (FRM) product disseminated by the LSA SAF. Besides assisting in wildfire management, the procedure is expected to help in decision making on prescribed burning within the framework of agricultural and forest management practices.

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Section: Statistical Models Of Exceedance Of Energy Released By Firesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fire danger rating over Mediterranean Europe based on fire radiative power derived from Meteosat

Pinto

DaCamara

Trigo

et al. 2018

Nat. Hazards Earth Syst. Sci.

View full text Add to dashboard Cite

show abstract

“…The selection of u is a selection over a univariate rv, and so any of the standard methods from the literature on univariate EVT for selecting the value of u may be employed, such as plots, mean-excess plots, etc. [11] While there is typically a region of in which u results in stable estimates of the GPD shape parameter ξ, making such univariate explorative techniques useful, useful, there is scope for Bayesian estimation of this threshold, for which the interested reader is directed to the surveys [8, 34, 35], which are mostly based on non-deterministic approximations, such as those involving MCMC.…”

Section: Concluding Discussionmentioning

confidence: 99%

Extending the Generalised Pareto Distribution for Novelty Detection in High-Dimensional Spaces

Clifton

Hugueny

et al. 2013

J Sign Process Syst

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Novelty detection involves the construction of a “model of normality”, and then classifies test data as being either “normal” or “abnormal” with respect to that model. For this reason, it is often termed one-class classification. The approach is suitable for cases in which examples of “normal” behaviour are commonly available, but in which cases of “abnormal” data are comparatively rare. When performing novelty detection, we are typically most interested in the tails of the normal model, because it is in these tails that a decision boundary between “normal” and “abnormal” areas of data space usually lies. Extreme value statistics provides an appropriate theoretical framework for modelling the tails of univariate (or low-dimensional) distributions, using the generalised Pareto distribution (GPD), which can be demonstrated to be the limiting distribution for data occurring within the tails of most practically-encountered probability distributions. This paper provides an extension of the GPD, allowing the modelling of probability distributions of arbitrarily high dimension, such as occurs when using complex, multimodel, multivariate distributions for performing novelty detection in most real-life cases. We demonstrate our extension to the GPD using examples from patient physiological monitoring, in which we have acquired data from hospital patients in large clinical studies of high-acuity wards, and in which we wish to determine “abnormal” patient data, such that early warning of patient physiological deterioration may be provided.

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“…The most common methods to estimate the unknown parameters of the GP distribution are the following: (i) the maximum likelihood (ML) method [15]; (ii) the method of moments [16]; (iii) the method of probability weighted moments [17]; (iv) the least squares (LS) method [18]; (v) the elemental percentile method [19] and (vi); the Bayesian technique, proposed by Castellanos and Cabras [20]. Bermudez and Kotz [21] made a review of the above-mentioned estimation methods. The selection of threshold is critical for the accurate estimation of the parameters of the GP distribution and in turn, return levels.…”

Section: Introductionmentioning

confidence: 99%

Directional Extreme Value Models in Wave Energy Applications

2020

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A wide range of wave energy applications relies on the accurate estimation of extreme wave conditions, while some of them are frequently affected by directionality. For example, attenuators and terminators are the most common types of wave energy converters whose performance is highly influenced by their orientation with respect to the prevailing wave direction. In this work, four locations in the eastern Mediterranean Sea are selected with relatively high wave energy flux values and extreme wave heights are examined with wave direction as a covariate. The Generalized Pareto distribution is used to model the extreme values of wave height over a pre-defined threshold, with its parameters being expressed as a function of wave direction through Fourier series expansion. In order to be consistent with the analysis obtained from the independent fits for directional sectors, the estimation of parameters is based on a penalized maximum likelihood criterion that ensures a good agreement between the two approaches. The obtained results validate the integration of directionality in extreme value models for the examined locations and design values of significant wave height are provided with respect to direction for the 50- and 100-year return period with bootstrap confidence intervals.

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Parameter estimation of the generalized Pareto distribution—Part II

Cited by 70 publications

References 35 publications

Fire danger rating over Mediterranean Europe based on fire radiative power derived from Meteosat

Fire danger rating over Mediterranean Europe based on fire radiative power derived from Meteosat

Extending the Generalised Pareto Distribution for Novelty Detection in High-Dimensional Spaces

Directional Extreme Value Models in Wave Energy Applications

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