A statistical test procedure for the shape parameter of a generalized Pareto distribution

Chaouche, Ali; Bacro, Jean-Noel

doi:10.1016/s0167-9473(03)00087-2

Cited by 14 publications

(8 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Si t 0 désigne la réalisation de T sur l'échantillon observé, on conclut quant au rejet ou non de H 0 selon la valeur de l'estimation empirique de Pr(T > t 0 ). La statistique de test utilisée est la statistique T 0 (Chaouche & Bacro, 2004) précédemment mentionnée.…”

Section: Signification Statistique Des Resultats Obtenus Pour Chaque unclassified

Incertitude d'estimation des pluies extrêmes du pourtour méditerranéen: illustration par les données de Marseille

Bacro

Chaouche²

2006

Hydrological Sciences Journal

Self Cite

View full text Add to dashboard Cite

Résumé Le modèle de renouvellement-dépassement est un modèle statistique fréquemment utilisé en hydrologie pour l'estimation de quantiles extrêmes. D'un point de vue théorique, cette modélisation stipule que les dépassements d'un seuil suffisamment élevé se distribuent, sous des hypothèses générales d'indépendance et d'homogénéité, selon une famille de lois paramétriques dites lois de Pareto généralisées, pour laquelle la loi exponentielle est un cas particulier. En pratique, très souvent, la loi exponentielle est imposée dans la modélisation et l'homogénéité n'est pas soumise à examen. L'importance pratique de ces hypothèses de modélisation est mise en évidence. L'ensemble de la démarche s'appuie sur les pluies journalières observées à Marseille durant 127 années. Des approches descriptives simples des cumuls journaliers à Marseille montrent que l'hypothèse d'homogénéité n'est pas admissible; admettre celle-ci conduit à minimiser les quantiles d'ordre élevé et peut avoir des conséquences dramatiques; si on s'en libère, ces quantiles augmentent considérablement et l'incertitude attachée à leur estimation, analysée dans cet article, rend tout à fait plausibles les records historiques observés en des sites du pourtour méditerranéen. On conclut en particulier que les pluies extrêmes à Marseille ne peuvent pas être assimilées à des réalisations d'une loi de Gumbel.Mots clefs distribution de Pareto généralisée; domaine d'attraction; hétérogénéité; modèle de renouvellement-dépassement; pluies extrêmes; quantiles Uncertainty in the estimation of extreme rainfalls around the Mediterranean Sea: an illustration using data from Marseille Abstract The peaks-over-threshold (POT) method is a usual statistical model for hydrologists working on extreme quantiles estimation. From a theoretical point of view, the model assumes, under some general hypotheses of independence and homogeneity, that the excesses over a sufficiently high threshold are distributed as a particular family of parametric laws called generalized Pareto distributions, of which the exponential distribution is a particular case. In practice, the exponential law is often imposed while the homogeneity is assumed. As shown in the paper, such model assumptions are of real importance for applications. A set of 127 years of daily rainfalls at Marseille is used to illustrate how to apply these assumptions in practice. Usual descriptive analysis shows the heterogeneity of the data. Assuming homogeneity leads to an underestimation of high quantiles, which could induce dramatic consequences in practice. Taking into account the data heterogeneity leads to a considerable increase of the estimated values. The uncertainty attached to these values, analysed in the paper, allows one then to reach some of the historical floods recorded in the Mediterranean region. A particular result is the following: the extreme daily rainfalls at Marseille are not in the Gumbel law domain.

show abstract

Section: Signification Statistique Des Resultats Obtenus Pour Chaque unclassified

Incertitude d'estimation des pluies extrêmes du pourtour méditerranéen: illustration par les données de Marseille

Bacro

Chaouche²

2006

Hydrological Sciences Journal

Self Cite

View full text Add to dashboard Cite

show abstract

“…We note that a statistical test of an exponential decay could also be applied to the tails of the chord length distributions; see, e.g. [4]. In conclusion our empirical analysis appears to indicate light tails of the chord length, and the result does not seem to be sensitive to the choice of a threshold or a covariance function.…”

Section: Application To the Chord Lengthsmentioning

confidence: 58%

How fast can the chord length distribution decay?

Demichel

Estrade

Kratz

et al. 2011

Advances in Applied Probability

View full text Add to dashboard Cite

Abstract. The modelling of random bi-phasic, or porous, media has been, and still is, under active investigation by mathematicians, physicists or physicians. In this paper we consider a thresholded random process X as a source of the two phases. The intervals when X is in a given phase, named chords, are the subject of interest. We focus on the study of the tails of the chord-length distribution functions. In the literature, different types of the tail behavior have been reported, among them exponential-like or power-like decay. We look for the link between the dependence structure of the underlying thresholded process X and the rate of decay of the chord-length distribution. When the process X is a stationary Gaussian process, we relate the latter to the rate at which the covariance function of X decays at large lags. We show that exponential, or nearly exponential, decay of the tail of the distribution of the chord-lengths is very common, perhaps surprisingly so.

show abstract

“…The GPD introduced independently by Balkema and De Haan (1974) and Pickands (1975) and as a limiting distribution function for scaled excesses over a high threshold has become one of the most useful concepts in the statistical analysis of extreme events (Chaouche and Bacro, 2004). If x is a random variable, the cumulative distribution function (CDF) of the GPD is defined as…”

Section: Gpdmentioning

confidence: 99%

“…However, Hosking and Wallis (1987) showed that really large samples are required (larger than 500 observations) for the MLE to provide acceptable results. For small sample sizes, the MLE does not give accurate estimations of the GPD parameters and sometimes does not even lead to any estimation at all (Chaouche and Bacro, 2004). However, for the problem at hand, a small sample size of thermal gradients is a common occasion because of the short-time implementation of SHM systems.…”

Section: Bayesian Estimation Combining Parameter Updatingmentioning

confidence: 99%

A generalized Pareto distribution–based extreme value model of thermal gradients in a long-span bridge combining parameter updating

Zhou

Chen

et al. 2016

Advances in Structural Engineering

View full text Add to dashboard Cite

Estimating extreme value models with high reliability for thermal gradients is a significant task that must be completed before reasonable thermal loads and possible thermal stress in long-span bridges are evaluated. In this article, a generalized Pareto distribution–based extreme value model combining parameter updating has been developed to describe the statistical characteristics of thermal gradients in a long-span bridge. The procedure of excluding correlation and the approach of selecting a proper threshold are suggested to prepare samples for generalized Pareto distribution estimation. A Bayesian estimation, which has the capability of updating model parameters by fusing prior information and incoming monitoring data, is proposed to fit the generalized Pareto distribution–based model. Furthermore, the Gibbs sampling, which is a Markov chain Monte Carlo algorithm, is adopted to derive the Bayesian posterior distribution. Finally, the proposed method is applied to the field monitoring data of thermal gradients in the Jiubao Bridge. The extreme value models of thermal gradients for the Jiubao Bridge are established, and the extreme thermal gradients with different return periods are extrapolated. The results indicate that the generalized Pareto distribution–based extreme value model has a strong ability to represent the statistical features of thermal gradients for the Jiubao Bridge, and the Bayesian estimation combining parameter updating provides high-precision generalized Pareto distribution–based models for predicting extreme thermal gradients. The predicted extreme thermal gradients are expected to evaluate and design long-span bridges.

show abstract

A statistical test procedure for the shape parameter of a generalized Pareto distribution

Cited by 14 publications

References 9 publications

Incertitude d'estimation des pluies extrêmes du pourtour méditerranéen: illustration par les données de Marseille

Incertitude d'estimation des pluies extrêmes du pourtour méditerranéen: illustration par les données de Marseille

How fast can the chord length distribution decay?

A generalized Pareto distribution–based extreme value model of thermal gradients in a long-span bridge combining parameter updating

Contact Info

Product

Resources

About