We consider a kernel-type nonparametric estimator of the intensity function of a cyclic Poisson process when the period is unknown. We assume that only a single realization of the Poisson process is observed in a bounded window which expands in time. We compute the asymptotic bias, variance, and the mean squared error of the estimator when the window indefinitely expands.

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Cyclic Poisson process, Intensity function, Linear trend, Nonparametric estimation, Consistency, Bias, Variance, Mean-squared error,

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Gamma-Pareto is a combination of Gamma and Pareto taking a form of Pareto composed in Gamma. With three parameters, Gamma-Pareto has more flexibility than Gamma or Pareto in accommodating the distribution of real data including rainfall data. Gamma distribution is widely used in various applications, such as modeling rainfall distribution. While Pareto, Generalized Pareto distribution (GPD) or Generalized Extreme Values distribution (GEV) are used to model extreme values, including extreme rainfall. As a development of Pareto distribution, Gamma-Pareto distribution may be considered as an alternative for modeling extreme rainfall. This paper discusses the application of Gamma-Pareto distribution (G-P) in modeling extreme rainfall. The Gamma-Pareto was applied to the monthly rainfall data from Jatiwangi station Jakarta with the observation period from January 1978 to March 2015. The results showed that the Gamma-Pareto was very appropriate for extreme monthly rainfall. For this data set, fitting using Gamma-Pareto was better than using Pareto, Gamma, and GPD distribution. Gamma-Pareto's return level was very good to predict the maximum monthly rainfall. 6030 Herlina Hanum et al.