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Echantillonnage par valeurs supérieures à un seuil : modélisation des occurrences par la méthode du renouvellement

Abstract : The principle of over-threshold sampling is to consider all the events in a time-series that exceed a given threshold. The probabilistic analysis implies estimating two statistical models, one describing the occurrence of events (date of the events), the other describing their magnitude (value of the local maximum). These two models are then combined to obtain the distribution of annual maximum flows. The theory of renewal processes can be used to study the occurrence of flood events. We present here properties of the well-known Poisson distribution (stationary or non-stationary process), and certain new results for the binomial and negative binomial distributions. The relationship between the distribution of a variable and its corresponding return period are then studied in more detail. Finally, we establish the analytical relationship between the two types of sampling, annual maximum sampling and peaks-over-threshold sampling, in terms of return period, distribution of the annual maximum, and sampling variance.
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Submitted on : Thursday, May 14, 2020 - 5:31:34 PM
Last modification on : Saturday, June 25, 2022 - 9:39:45 PM

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  • HAL Id : hal-02575992, version 1
  • IRSTEA : PUB00002770

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M. Lang, P. Rasmussen, G. Oberlin, B. Bobée. Echantillonnage par valeurs supérieures à un seuil : modélisation des occurrences par la méthode du renouvellement. Journal of Water Science / Revue des Sciences de l'Eau, Lavoisier (Hermes Science Publications), 1997, pp.279-320. ⟨hal-02575992⟩

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