A note of caution when interpreting parameters of the distribution of excesses

Ribereau, Pierre; Naveau, Philippe; Guillou, Armelle

doi:10.1016/j.advwatres.2011.05.003

Cited by 13 publications

(7 citation statements)

References 15 publications

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“…In Section 3.1, we notice that the random variable

V = σ H_{ξ} ((), G false(Z false))

always follows the generalized Pareto H ξ (./ σ ). In hydrology, there is a long history of using the so‐called probability‐weighted moments (PWMs) to infer the parameters of a GPD (see, e.g., Carreau, Naveau, & Neppel, ; Hosking & Wallis, ; Naveau et al, ; Ribereau et al, ). The PWM estimation method is easy to understand, fast, robust, and efficient (if ξ <0.5, a reasonable assumption for our rainfall data).…”

Section: Methodology For Fitting a Semiparametric Egpd Modelmentioning

confidence: 99%

“…The red flag pointing toward an overestimation of could be the scatterplot between the estimates of and obtained by bootstrapping the original rainfall data (before thresholding). This last plot indicates that the variability in the estimation of can be large, ranging from zero to 0.8, and the clear negative correlation between the estimators of and is a well known feature of the GP parameter inference, that is, an overestimation of is coupled by an underestimation of and vice-versa (see, e.g., Ribereau, Naveau, & Guillou, 2011). As it is operationally impossible to repeat this visual inspection for our 180 weather stations and for different threshold values, this leaves us to wonder if the large estimate of for the Chartres station is just due to the inherent variability of GP fit for small samples (here, 40 exceedances above the 95% threshold).…”

Section: Introductionmentioning

confidence: 94%

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Flexible semiparametric generalized Pareto modeling of the entire range of rainfall amount

et al. 2019

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Precipitation amounts at daily or hourly scales are skewed to the right, and heavy rainfall is poorly modeled by a simple gamma distribution. An important yet challenging topic in hydrometeorology is to find a probability distribution that is able to model well low, moderate, and heavy rainfall. To address this issue, we present a semiparametric distribution suitable for modeling the entire range of rainfall amount. This model is based on a recent parametric statistical model called the class of extended generalized Pareto distributions (EGPDs). The EGPD family is in compliance with extreme value theory for both small and large values, while it keeps a smooth transition between these tails and bypasses the hurdle of selecting thresholds to define extremes. In particular, return levels beyond the largest observation can be inferred. To add flexibility to this EGPD class, we propose to model the transition function in a nonparametric fashion. A fast and efficient nonparametric scheme based on Bernstein polynomial approximations is investigated. We perform simulation studies to assess the performance of our approach. It is compared to two parametric models: a parametric EGPD and the classical generalized Pareto distribution (GPD), the latter being only fitted to excesses above a high threshold. We also apply our semiparametric version of EGPD to a large network of 180 precipitation time series over France.

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“…In Section 3.1, we notice that the random variable

V = σ H_{ξ} ((), G false(Z false))

Section: Methodology For Fitting a Semiparametric Egpd Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 94%

Flexible semiparametric generalized Pareto modeling of the entire range of rainfall amount

et al. 2019

View full text Add to dashboard Cite

show abstract

“…Also, the shape and scale panels are almost symmetric: a posterior distribution granting most weight to comparatively high shape parameters concentrates on comparatively low scales. This corroborates the fact that frequentist estimates of the shape and the scale parameter are negatively correlated [ Ribereau et al ., ]. In the regional model as well as in the local one, the posterior variance of each parameter is reduced when taking into account historical data (except for the scale parameter at Anduze, for the local model).…”

Section: Resultsmentioning

confidence: 99%

Combining regional estimation and historical floods: A multivariate semiparametric peaks‐over‐threshold model with censored data

Sabourin

Renard²

2015

Water Resources Research

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The estimation of extreme flood quantiles is challenging due to the relative scarcity of extreme data compared to typical target return periods. Several approaches have been developed over the years to face this challenge, including regional estimation and the use of historical flood data. This paper investigates the combination of both approaches using a multivariate peaks-over-threshold model that allows estimating altogether the intersite dependence structure and the marginal distributions at each site. The joint distribution of extremes at several sites is constructed using a semiparametric Dirichlet Mixture model. The existence of partially missing and censored observations (historical data) is accounted for within a data augmentation scheme. This model is applied to a case study involving four catchments in Southern France, for which historical data are available since 1604. The comparison of marginal estimates from four versions of the model (with or without regionalizing the shape parameter; using or ignoring historical floods) highlights significant differences in terms of return level estimates. Moreover, the availability of historical data on several nearby catchments allows investigating the asymptotic dependence properties of extreme floods. Catchments display a significant amount of asymptotic dependence, calling for adapted multivariate statistical models.

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“…The parameter ν is less correlated with the other parameters, although there is a noticeable positive correlation with ξ. In applications, the end user is generally interested in return levels, which are functions of the four parameters of the model, and, thus, the errors made on individual parameters may compensate for one another [see also Ribereau, Naveau and Guillou (2011)]. Figure 10 compares various important characteristics of the extremal behavior of the data with those of the fitted model.…”

Section: 2mentioning

confidence: 99%

Modeling extreme values of processes observed at irregular time steps: Application to significant wave height

Raillard¹,

Ailliot²,

Yao

2014

Ann. Appl. Stat.

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This work is motivated by the analysis of the extremal behavior of buoy and satellite data describing wave conditions in the North Atlantic Ocean. The available data sets consist of time series of significant wave height (Hs) with irregular time sampling. In such a situation, the usual statistical methods for analyzing extreme values cannot be used directly. The method proposed in this paper is an extension of the peaks over threshold (POT) method, where the distribution of a process above a high threshold is approximated by a max-stable process whose parameters are estimated by maximizing a composite likelihood function. The efficiency of the proposed method is assessed on an extensive set of simulated data. It is shown, in particular, that the method is able to describe the extremal behavior of several common time series models with regular or irregular time sampling. The method is then used to analyze Hs data in the North Atlantic Ocean. The results indicate that it is possible to derive realistic estimates of the extremal properties of Hs from satellite data, despite its complex space-time sampling.

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A note of caution when interpreting parameters of the distribution of excesses

Cited by 13 publications

References 15 publications

Flexible semiparametric generalized Pareto modeling of the entire range of rainfall amount

Flexible semiparametric generalized Pareto modeling of the entire range of rainfall amount

Combining regional estimation and historical floods: A multivariate semiparametric peaks‐over‐threshold model with censored data

Modeling extreme values of processes observed at irregular time steps: Application to significant wave height

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