Στατιστική ανάλυση και προβλέψεις σε περιβαλλοντολογικά μοντέλα με τη χρήση της θεωρίας ακραίων τιμών

Παρτσακουλάκης, Βασίλειος Ε.

Master Thesis

Author

Παρτσακουλάκης, Βασίλειος Ε.

Date

2012-10-24

Abstract

In the last years, the contribution of extreme value theory in prediction and prevention of extreme environmental phenomena is very crucial, resulting to the prevention of huge natural and economic disasters. The main target of this dissertation is to present statistical methods from extreme value theory, appropriate for the statistical analysis of extreme environmental data. Initially, it presents the basic probabilistic results from extreme value theory and the main statistical method of analyzing extremes (Block Maxima) for stationary observations. Next, it analyzes the special features and properties of environmental extreme data, such as time dependence, seasonality and trend, and show how these characteristics can be modeled in the context of extreme value theory. Subsequently, it empirically studies the performance of MLE’s of Block Maxima method (incorporating seasonality and trend) that was developed for the study of environmental extremes. Two data sets are being used for the application of the statistical models presented. The first set contains extreme precipitations of 21 meteorological stations over Greece for a time period of 50 years, and the second set contains extreme high temperatures of 18 meteorological stations over Greece for the same time period. For all necessary computations and numerical estimations it uses the software package R (www.r-project.org/). More specifically it estimates the parameters of the models which were developed in the previous sessions, as well as the monthly return level for 10 and 50 years (and also compute the respective variance of estimates). Finally, it discusses qualitative conclusions about the method it used and some general conclusions about extreme precipitation and temperature in Greece.