Distribution Theories And Applications Of Extreme Statistic For Time Series Relative To The Initial Value

Extreme events are rarer than those already recorded, but profound influences are producedwhen they occur. The theory of extreme value is a branch of order statistics. The production anddevelopment of extreme value theory provide theoretical bases for these random events. And thetheory of extreme value traditionally can be used as a tool forecasting tsunami, earthquake andflood. Recently it has been applied to financial risk management.Now, climatic issues such as global warming are becoming serious. Investigating andanalyzing meteorological data is therefore making more sense. But in the whole world climaticchange researches, the research of 'the extreme climates' is still weak, how to describe andmonitor extreme climates or to performance extreme climatic statistical characteristics and thechanged rules, became one of important topics about climatic change research. At present, wemainly have two models in the extreme value analysis. One is extreme value theorem model(EVT), this model is mainly used to the group in the maximum value modeling. The extremevalue theorem has guaranteed that the limit distribution is belonged to one of the three extremevalue distributions which are termed as the Frechet, Weibull and Gumbel distribution, we mayuse unification of the original three families of extreme value distribution into a single familygeneralizedextreme value (GEV) family of distributions; Another is the generalized Paretodistribution model, this model is used to establish model when the data exceed some highthreshold, then threshold excesses have a corresponding approximate distribution within thegeneralized Pareto family.At first, this dissertation mainly introduced the three limit distributions of extreme valuetheorem and the correlation contents, then introduced threshold models, gave the maximum valuemodel of the generalized Pareto distribution and the minimum generalized Pareto distribution.Application and forecast in the temperature are introduced to use maximum value model of thegeneralized Pareto, the theories of extreme value index estimate are introduced as well as several methods of threshold value selection, and discussed some related properties. Finally, we obtainedthe desirable result: the theory of extreme statistical distribution of the maximum and minimumrelative to the initial value.