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An extension of the Yule process for the stochastic modelling of recurrent events. Application to the failures of pressure water mains.

Yves Le Gat
Abstract : An extension of the Yule Process is proposed that aims at stochastically modelling recurrent events. The analytical form of the distribution of the number of events in a given time interval conditional on the number of past events is established; this distribution is important for modelling an actual process observed within any bounded time interval. The linear dependency between process intensity and rank of event leads to a negative binomial distribution. The likelihood function of the LEYP model (Linear Extended Yule Process) given a sequence of observed events is built, and allows to estimate the parameters. The number of events in a time interval given the number of events in a previous interval is then proven to also have a negative binomial distribution; this result is essential to validate the model and perform predictions. If the system lifetime is randomly limited due to past events, data may be biased by the selective survival phenomenon, and the system survival has to considered when building the likelihood function. The model parameter estimation is studied by computer simulations. It is shown how to simulate a sample of events distributed according to a LEYP, estimate the parameters by maximizing their likelihood function, perform predictions, and validate them by building a predictive performance curve. The LEYP model is lastly used with real failure data, that demonstrate its practical efficiency.
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Submitted on : Wednesday, April 14, 2010 - 8:00:00 AM
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Yves Le Gat. An extension of the Yule process for the stochastic modelling of recurrent events. Application to the failures of pressure water mains.. Engineering Sciences [physics]. ENGREF (AgroParisTech), 2009. English. ⟨NNT : 2009AGPT0061⟩. ⟨pastel-00005992⟩

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