New Statistical models for Extreme Values

UoM administered thesis: Phd

  • Authors:
  • Sumaya Eljabri

Abstract

Extreme value theory (EVT) has wide applicability in several areas like hydrology, engineering, science and finance. Across the world, we can see the disruptive effects of flooding, due to heavy rains or storms. Many countries in the world are suffering from natural disasters like heavy rains, storms, floods, and also higher temperatures leading to desertification. One of the best known extraordinary natural disasters is the 1931 Huang He flood, which led to around 4 millions deaths in China; these were a series of floods between Jul and Nov in 1931 in the Huang He river.Several publications are focused on how to find the best model for these events, and to predict the behaviour of these events. Normal, log-normal, Gumbel, Weibull, Pearson type, 4-parameter Kappa, Wakeby and GEV distributions are presented as statistical models for extreme events. However, GEV and GP distributions seem to be the most widely used models for extreme events. In spite of that, these models have been misused as models for extreme values in many areas.The aim of this dissertation is to create new modifications of univariate extreme value models.The modifications developed in this dissertation are divided into two parts: in the first part, we make generalisations of GEV and GP, referred to as the Kumaraswamy GEV and Kumaraswamy GP distributions. The major benefit of these models is their ability to fit the skewed data better than other models. The other idea in this study comes from Chen, which is presented in Proceedings of the International Conference on Computational Intelligence and Software Engineering, pp. 1-4. However, the cumulative and probability density functions for this distribution do not appear to be valid functions. The correction of this model is presented in chapter 6.The major problem in extreme event models is the ability of the model to fit tails of data. In chapter 7, the idea of the Chen model with the correction is combined with the GEV distribution to introduce a new model for extreme values referred to as new extreme value (NEV) distribution. It seems to be more flexible than the GEV distribution.

Details

Original languageEnglish
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Award date1 Aug 2013