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Abstract
In this thesis, we focus on statistical modelling for extreme precipitation of the Colombo region in Sri Lanka, and to estimate the return levels for various return periods. The basic data consists of the daily precipitation during the period of 110 years from 1900 to 2009 and obtained from the Colombo station. The Generalized Extreme Value (GEV) distribution is fitted according to the Block Maxima approach using annual maximum rainfall whereas, the daily rainfall values exceeding a given threshold value is modelled by the Peak-Over-Threshold method and fitted to the Generalized Pareto (GP) distribution. The parameters of the models are estimated by method of Maximum Likelihood Estimation (MLE) while the diagnostic plots and Kolmogorov-Smirnov (KS) test are used to evaluate the performance of both models. Specifically, the bootstrap goodness-of-fit test is carried out to scrutinize the sign of the Shape (?) parameter of the GP distribution. The likelihood ratio test has been used to evaluate the best model from the GEV and GP distribution. Results show that both GEV and GP distribution yield very similar results, however the GEV distribution has a greater amount of uncertainty than the GP model. It was found that the return levels for extreme precipitation have increased over time. We recommend that these results can be used as a guide when developing an infrastructure and early warning system for the city.
