A Poisson-cluster model of rainfall: some high-order moments and extreme values

Abstract
A conceptual stochastic model for rainfall, based on a Poisson-cluster process with rectangular pulses representing rain cells, is further developed. A method for deriving high-order moments is applied to obtain the third-moment function for the model. This is used with second-order properties to fit the model to January and July time-series taken from a site in Wellington, New Zealand. It is found that the parameter estimates may follow two solution paths converging on an optimum value over a bounded interval. The parameter estimates are used with the model to simulate 200 years of hourly data, and parametric tests used to compare simulated and observed extreme rainfalls. These show good agreement over a range of sampling intervals. The paper concludes with a discussion of the standard errors of the model parameter estimates which are obtained using a non-parametric bootstrap.

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