Stochastic Models of Temporal Rainfall: Reproducibility, Estimation and Prediction of Extreme Events

Temporal rainfall models based on the point-process theory are reviewed. First the compound Poisson approach is examined. Theoretical analysis concerned with the extreme properties is presented for the Independent Poisson Marks model, and an example of application to the real world is discussed. The clustered Poisson approach with rectangular pulses is then analyzed in terms of both the Neyman-Scott model, and the Bartlett-Lewis one. The available theoretical work is reviewed, and some problems arising in statistical inference are further analyzed. Criteria of model fitting and parameter estimation are also presented in the light of applications to real-world hydrology. Finally, an extensive field data analysis is presented, in order to assess the capability of the mathematical models investigated to represent the actual behaviour of the natural process.

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