Extreme Value Distribution Model And Its Application In Geochemical Exploration Data Analysis

Extreme value theory is an important branch of mathematical statistics whichfocus on the studies of distribution of limit about the maximum and the minimum(collectively referred to as the extreme). This theory is mainly used to evaluate andforecast the risk of extreme events. It has been widely used in the fields ofmeteorological, flood, earthquake, insurance and Finance and so on. In geological,compared to geological background value, the extreme value of the geochemical datacan be considered to be geological anomaly. Abnormal observed value lies at the endof the distribution.And extreme value analysis no other than the study on paranormalbig (or small) level quantitative process of random characters. Therefore, themathematical foundation of geological anomalies is the extreme value theory.This paper mainly studies the modeling method of the extreme value statisticsand the parameter estimation or the test of fitting effect of the generalized paretodistribution model. And with shandong large grinding composer and Big YinGezhuang ore-forming elements and its storage to be as the research objects.In orderto discuss the application of the extreme value theory which has been used in theaspects of geochemical anomaly recognition, outliers probability distribution fittingand prediction reserves. This thesis is focus on the following aspects:Firstly, systematically introduce the methods of Extreme value theory and itsclassification, parameter estimation and model test. Compared the BMM model withthe POT model of extreme value theory,we found the superiority of POT model, so, inthis article, we mainly adopt the POT model.Secondly, in view of the generalized pareto distribution parameter estimationmethod, the maximum likelihood estimation method to get the likelihood equation isnonlinear transcendental equation and it has no characteristic of analytical solution,So I put forward an approximate analytical solution of the improved estimationmethod which possess the analytical solution. In addition, I proved that thegeneralized pareto distribution has the characteristics of Fractal invariance.Thirdly, based on the POT model to put forward the methods and steps aboutgeological anomaly recognition and statistical modeling. Fourthly, Using the empirical analysis research on geochemical data of the fourelements, they are Shandong great composer Zn, Cu, Ag, and As. Integrated use ofmean exceed function method and Hill diagram, and combining the GramervostatisticW2and Anderson-Darling statisticA2test, to determine the geochemicaldata of the anomaly threshold u. Through the proposed approximate parameterestimation method to estimate the model parameter. Then establish the probabilitydistribution of the abnormal value, and conduct the fitting inspection.