干旱历时与干旱烈度的尾部相关性分析
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摘要
针对干旱频率分析中干旱历时与干旱烈度两变量间的尾部相关性问题,基于四川省30个代表性站点1958~2012年的逐月降雨资料,采用SEC法计算了各站点干旱历时与干旱烈度的经验尾部相关系数,分析了Archimedean Copula函数在描述干旱变量尾部相关性时的差异。结果表明,四川省干旱历时与干旱烈度的上尾相关系数介于0~1之间,下尾相关系数为0,因此该地区干旱历时与干旱烈度上尾相关,下尾渐近独立;Archimedean Copula函数族中Clayton、Frank和Gumbel三种函数的对比分析表明,仅Gumbel Copula函数能较好地描述两变量间的上尾部相关性,其他函数效果不佳。
Aiming at the tail dependence between drought duration and drought severity in drought frequency analysis,based on the monthly rainfall series of 30typical stations in Sichuan Province from 1958to 2012,the SEC method was adopted to estimate the empirical tail-dependence coefficients of drought events.The differences among Archimedean Copula functions in describing the tail dependence were analyzed.The results show that the upper tail-dependence coefficient's values lies between 0and 1,and the lower tail-dependence coefficient is equal to zero;the tail dependence between drought duration and drought severity in the area is just the upper tail dependence;Gumbel-Hougaard function can express the upper tail dependence between drought duration and drought severity well,but Clayton and Frank can not do the same thing.
Aiming at the tail dependence between drought duration and drought severity in drought frequency analysis,based on the monthly rainfall series of 30typical stations in Sichuan Province from 1958to 2012,the SEC method was adopted to estimate the empirical tail-dependence coefficients of drought events.The differences among Archimedean Copula functions in describing the tail dependence were analyzed.The results show that the upper tail-dependence coefficient's values lies between 0and 1,and the lower tail-dependence coefficient is equal to zero;the tail dependence between drought duration and drought severity in the area is just the upper tail dependence;Gumbel-Hougaard function can express the upper tail dependence between drought duration and drought severity well,but Clayton and Frank can not do the same thing.
引文
[1]闫海梅,王波,韩艳艳.基于Copula理论的尾部相关性分析[J].统计与决策,2011(21):149-152.
[2]王晓丽,席金平,吴润衡.基于Copula函数和非参数估计的尾部相关性[J].数学的实践与认识,2009,39(7):54-57.
[3]郭生练,闫宝伟,肖义,等.Copula函数在多变量水文分析计算中的应用及研究进展[J].水文,2008,28(3):1-7.
[4]Frahm G,Junker M,Schmidt R.Estimating the Tail Dependence Coefficient:Properties and Pitfalls[J].Mathematics and Economics,2005,37(1):80-100.
[5]闫宝伟,郭生练,陈璐,等.Copula函数在水文计算中的适用性分析[J].数学的实践与认识,2012,42(3):85-93.
[6]周玉良,袁潇晨,金菊良,等.基于Copula的区域水文干旱频率分析[J].地理科学,2011,31(11):1 383-1 388.
[2]王晓丽,席金平,吴润衡.基于Copula函数和非参数估计的尾部相关性[J].数学的实践与认识,2009,39(7):54-57.
[3]郭生练,闫宝伟,肖义,等.Copula函数在多变量水文分析计算中的应用及研究进展[J].水文,2008,28(3):1-7.
[4]Frahm G,Junker M,Schmidt R.Estimating the Tail Dependence Coefficient:Properties and Pitfalls[J].Mathematics and Economics,2005,37(1):80-100.
[5]闫宝伟,郭生练,陈璐,等.Copula函数在水文计算中的适用性分析[J].数学的实践与认识,2012,42(3):85-93.
[6]周玉良,袁潇晨,金菊良,等.基于Copula的区域水文干旱频率分析[J].地理科学,2011,31(11):1 383-1 388.