Statistical modeling of extremes under linear and power normalizations with applications to air pollution
Keywords:
Air pollution, bootstrap technique, generalized extreme value model, generalized Pareto distribution, Kolmogorov-Smirnov testAbstract
In this paper the Block Maxima (BM) and the Peak Over Threshold (POT) methods are used to model the air pollution in two cities in Egypt. A simulation technique is suggested to choose a suitable threshold value. The validity of full bootstrapping technique for improving the estimation parameters in extreme value models has been checked by Kolmogorov-Smirnov (K-S) test. A new efficiency approach for modeling extreme values is suggested. This approach can convert any ordered data to enlarged block data by using sub-sample bootstrap. By using power normaliziation, for the first time in litrarure, the BM and sub-sample bootstrap methods are applied to model the air pollution. Although, this study is applied on three pollutants in two cities in Egypt, the suggested approaches may be applied on other pollutants in other regions in any country.
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