Unbiased parameter estimation of the Neyman-Scott model for rainfall simulation with related confidence interval

The Neyman-Scott rectangular pulses model is a clustered point process in time. This article presents a new method of parameters estimation for this model applied to rainfall simulation. It is based on a modified method of moments using two temporal scales of aggregation. A simple algebraic computation leads to reduce the number of parameters estimated by minimisation. Indeed two parameters are obtained by minimisation while the three others can be directly computed. The optimisation method used is based on the Nelder-Mead simplex. The minimisation procedure is stable with regard to the starting point and always converges. The related approximate confidence interval is obtained using the delta method and block bootstrap techniques. The validation is carried out using the rainfall station of Payerne situated on the Swiss Plateau. 100series of 10 years of hourly rainfall have been generated for both a summer and a winter month. From the obtained simulated series 100 sets of parameters have been determined. These parameters estimators are unbiased.