A flexible extended generalized Pareto distribution for tail estimation

Gamet, Philémon; Jalbert, Jonathan

doi:10.1002/env.2744

Cited by 9 publications

(5 citation statements)

References 32 publications

(59 reference statements)

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“…It is also possible to apply (2) to various extensions of the GPD whose greater flexibility may allow one to use lower thresholds (Gamet and Jalbert, 2022).…”

Section: Methodsmentioning

confidence: 99%

A weighted composite log-likelihood approach to parametric estimation of the extreme quantiles of a distribution

Stein

2023

Extremes

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Extreme value theory motivates estimating extreme upper quantiles of a distribution by selecting some threshold, discarding those observations below the threshold and fitting a generalized Pareto distribution to exceedances above the threshold via maximum likelihood. This sharp cutoff between observations that are used in the parameter estimation and those that are not is at odds with statistical practice for analogous problems such as nonparametric density estimation, in which observations are typically smoothly downweighted as they become more distant from the value at which the density is being estimated. By exploiting the fact that the order statistics of independent and identically distributed observations form a Markov chain, this work shows how one can obtain a natural weighted composite log-likelihood for fitting generalized Pareto distributions to exceedances over a threshold. Some theory demonstrates the asymptotic advantages of using weights in the special case when the shape parameter of the limiting generalized Pareto distribution is known to be 0. Methods for extending this approach to observations that are not identically distributed are described and applied to an analysis of daily precipitation data in New York City. Perhaps the most important practical finding is that including weights in the composite log-likelihood can reduce the sensitivity of estimates to small changes in the threshold.

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“…It is also possible to apply (2) to various extensions of the GPD whose greater flexibility may allow one to use lower thresholds (Gamet and Jalbert, 2022).…”

Section: Methodsmentioning

confidence: 99%

A weighted composite log-likelihood approach to parametric estimation of the extreme quantiles of a distribution

Stein

2023

Extremes

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“…This approach has been applied and tested in various contexts (e.g. Haruna et al, 2023;Gamet & Jalbert, 2022;Rivoire et al, 2021;Legrand et al, 2023).…”

Section: Extreme Value Modellingmentioning

confidence: 99%

Strong linkage between observed daily precipitation extremes and anthropogenic emissions across the contiguous United States

S.,

Villarini,

Kim

et al. 2024

Preprint

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The results of probabilistic event attribution studies depend on the choice of the extreme value statistics used in the analysis, particularly with the arbitrariness in the selection of appropriate thresholds to define extremes. We bypass this issue by using the Extended Generalized Pareto Distribution (ExtGPD), which jointly models low precipitation with a generalized Pareto distribution and extremes with a different Pareto tail, to conduct daily precipitation attribution across the contiguous United States (CONUS). We apply the ExtGPD to 12 general circulation models from the Coupled Model Intercomparison Project Phase 6 and compare counterfactual scenarios with and without anthropogenic emissions. Observed precipitation by the Climate Prediction Centre is used for evaluating the GCMs. We find that greenhouse gases rather than natural variability can explain the observed magnitude of extreme daily precipitation, especially in the temperate regions. Our results highlight an unambiguous linkage of anthropogenic emissions to daily precipitation extremes across CONUS.

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“…Therefore, to enlighten the structure of the OGEV distribution, quantile-based OGEV distribution aliases are approximated by the (𝜆, 𝛽) parameter plane using Galton's skewness (Galton, 1883) and Moor's kurtosis (Moors, 1988) defined by the following formulas. Galton's measure of skewness (−1 ≤ S ≤ 1) is defined in (Gilchrist, 2000) as, S = (Upper quartile − Median) + (Lower quartile − Median) Interquartile distance .…”

Section: The Ogev Aliases Of Some Extreme Value Distributionsmentioning

confidence: 99%

“…Extremes of climate variables are essential to researchers due to their impact on social and economic activities. For instance, extreme temperatures, precipitation, and heat waves are vital for planning and making policies because of their effects on different sectors of the economy (Gamet & Jalbert, 2022). Numerous adverse effects of increasing temperatures on economic growth emanate from their negative impact on health and productivity.…”

Section: Introductionmentioning

confidence: 99%

New generalized extreme value distribution with applications to extreme temperature data

Gyasi,

Cooray

2023

Environmetrics

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A new generalization of the extreme value distribution is presented with its density function, having a wide variety of density and tail shapes for modeling extreme value data. This generalized extreme value distribution will be referred to as the odd generalized extreme value distribution. It is derived by considering the distributions of the odds of the generalized extreme value distribution. Consequently, the new distribution is enlightened by not only having all six families of extreme value distributions; Gumbel, Fréchet, Weibull, reverse‐Gumbel, reverse‐Fréchet, and reverse‐Weibull as submodels but also convenient for modeling bimodal extreme value data that are frequently found in environmental sciences. Basic properties of the distribution, including tail behavior and tail heaviness, are studied. Also, quantile‐based aliases of the new distribution are illustrated using Galton's skewness and Moor's kurtosis plane. The adequacy of the new distribution is illustrated using well‐known goodness‐of‐fit measures. A simulation is performed to validate the estimated risk measures due to repeated data points frequently found in temperature data. The Grand Rapids and well‐known Wooster temperature data sets are analyzed and compared to nine different extreme value distributions to illustrate the new distribution's bimodality, flexibility, and overall fitness.

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A flexible extended generalized Pareto distribution for tail estimation

Cited by 9 publications

References 32 publications

A weighted composite log-likelihood approach to parametric estimation of the extreme quantiles of a distribution

A weighted composite log-likelihood approach to parametric estimation of the extreme quantiles of a distribution

Strong linkage between observed daily precipitation extremes and anthropogenic emissions across the contiguous United States

New generalized extreme value distribution with applications to extreme temperature data

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