二元超阈值模型在环境中的应用

The Application of Bivariate Threshold Excess Model in the Atmospheric Environment

近年来,随着现代工业和交通运输业的飞速发展,大气中排放物的数量越来越多,种类也越来越复杂,产生了越来越严重的大气环境污染。本文主要研究二元超阈值方法及其在大气环境中的应用。研究二元极值分布,除了要知道各个变量的边缘分布,还需要知道两个变量之间的尾部相关性。给出了两种度量随机变量尾部相关性的方法,并将其应用于上海市大气环境指标中,发现可吸入颗粒物API与二氧化硫API具有较强的尾部相关性。为了更深入地了解两个指标间的尾部相关性及其两个指标的走势,建立了二元超阈值模型。首先,根据阈值模型建立了每个指标的分布函数。然后,选取不对称Logis-tic模型作为可吸入颗粒物API与二氧化硫API的相关结构函数,构造出了两个指标的尾部联合分布,并对未来两个指标的走向进行分析和预测。

In recent years,more and more air pollutants have been discharged into the atmosphere.When pollutants in the atmosphere reach a certain amount,some kinds of air pollution events would happen.The bivariate threshold excess model and its application in atmospheric environment are mainly studied.When studying the extremes values of two variables,each variable can be modeled using univariate techniques,however,the extreme value inter-relationships would also be needed to study.A measure to study tail correlation between two variables is given.Then it was applied to the indicators of atmospheric environment in Shanghai.The result is that APIs for respirable particulate matter and for sulfur dioxide have a stronger tail dependence.In order to get a better understanding of two indicators,a bivariate threshold excess model is need to build.Firstly,distribution function for every index is established.Secondly,asymmetric Logistic model is selected as the structure functions for APIs of respirable particulate matter and sulfur dioxide.Then with this functions distribution of two indexes in case of exceeding the threshold is established,which can be used to analysis and forecast how the two indexes change in future.