Modeling extreme rainfall with Gamma-Pareto distribution

Abstract

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.

Evolving extreme events caused by climate change: A tail based Bayesian approach for extreme event risk analysis

“…Parameter range estimate: The HRTD parameter range is estimated through the Hill 23 and SmooHill 24 estimators, and estimated values are listed in Table 2. The details of the implementation of the Hill and SmooHill estimators are described in.…”

“…A tail based approach has been proposed by Arif et al, 19 and considering the 1000 year return period to capture most extreme scenarios. A similar approach was also proposed by Clauset and Woodard 20 The Monte Carlo method 21,22 and the Mixer model 23 have been considered in past research for rare event modelling. Model parameter estimation in the case of an unusual event may not be straightforward.…”

The Application of Modeling Gamma-Pareto Distributed Data Using GLM Gamma in Estimation of Monthly Rainfall with TRMM Data

“…The distribution shows a better fit than some distributions for three types of data by [1]. While [2] used G-P distribution in modeling monthly extreme rainfall. The application of G-P distribution is still limited for modeling single variable data.…”

“…Fitting data begins with parameter estimation of the certain distribution based on the data. Parameter estimation of G-P follows the method in [1] and [2]. Based on the estimator of the G-P parameter, then we determined the quantile values of G-P using quantile function of G-P in [2].…”

“…Parameter estimation of G-P follows the method in [1] and [2]. Based on the estimator of the G-P parameter, then we determined the quantile values of G-P using quantile function of G-P in [2]. Kolmogorov-Smirnov test [8] is used to assess the goodness of fit between data and quantile values.…”