Theoretical discussion and Monte-Carlo simulations for a Negative Binomial process paradox |
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| Authors: | M Lang |
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| Institution: | (1) Cemagref Lyon, Division Hydrologie-Hydraulique, 3bis quai Chauveau, 69336 Lyon cedex 09, France Phone: 33 (0) 4 72 20 87 98, Fax: 33 (0) 4 78 47 78 75, e-mail: michel.lang@cemagref.fr, FR |
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| Abstract: | The idea of an over-threshold sampling is to retain all the events of a time-series exceeding a given threshold. The probabilistic
analysis implies estimating two statistical models, one describing the occurrence of the 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 the annual maxima. A well-known result of a Poisson process is that waiting time, defined as the duration between two successive
events exceeding the threshold, is exponentially distributed. The assertion that the waiting time of a Negative Binomial process
is also exponentially distributed seems to be in obvious contradiction with the Poisson process properties. A theoretical
discussion and Monte-Carlo simulations are presented to solve this apparent paradox. |
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| Keywords: | : Negative Binomial distribution Flood Frequency Analysis Occurrence process Monte Carlo simulation Waiting Time distribution |
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