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Distribution Theories and Applications of Extreme Statistic for Time Series Relative to the Initial Value

Author: YuXiYa
Tutor: ZongXuPing
School: Yangzhou University
Course: Probability Theory and Mathematical Statistics
Keywords: Generalized extreme value distribution Generalized Pareto Distribution Threshold Maximum likelihood estimation Extreme value index
CLC: O211.3
Type: Master's thesis
Year: 2010
Downloads: 84
Quote: 1
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Abstract


In the range of cognitive , fewer extreme events , however, the effect of the event is material . Extreme value theory is a branch , the emergence and development of the statistical theory of extreme order statistics , provides a theoretical basis for the statistical analysis of such random events , have traditionally been used to predict tsunamis, earthquakes , floods and other natural disasters , in recent years has been widely used in the management of financial risks . With the increasingly serious problem of global warming and climate research and analysis of meteorological data has become increasingly important significance for the production practices and social life , and in the study of global climate change , \links, how to describe and monitor extreme weather or performance of Extreme Climate various statistical characteristics and its variation , has become one of the important issue of climate change research . Extreme value analysis are mainly two types of models , a class of extreme value theorem model ( EVT ) , the maximum modeling , such models on group extremal type theorem guarantees maximum limit distribution group for three one of the extreme value distribution , ie Frechet distribution , Weibull distribution and the Gumbel distribution can also use their unified form - generalized extreme value distribution (GEV) analysis ; another type of generalized Pareto distribution model , its observations over a larger threshold data modeling , the asymptotic distribution of the Generalized Pareto distribution family . This paper first introduces three limit distribution of extreme value theory and its content , and then introduce a threshold excess model , given the generalized Pareto distribution of the maximum value and the minimum value of the generalized Pareto distribution , and the maximum value of the empirical analysis shows Generalized Pareto distribution in extreme temperatures forecast ; then introduced extreme value index estimation theory and the several threshold selection method , and discuss some of them related to the nature ; Finally, with respect to the initial value of the time series of extreme distribution the extreme statistical theory , and the theory was combined with the actual data it in extreme temperatures forecast and achieve better results .

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CLC: > Mathematical sciences and chemical > Mathematics > Probability Theory and Mathematical Statistics > Theory of probability ( probability theory, probability theory ) > Distribution theory
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