四参数二元McKay型伽马分布的几个性质

Some properties of the four-parameter McKay's bivariate gamma distribution

讨论了四参数二元McKay型伽马分布的几个性质.通过变量替换技术,导出了四参数二元McKay型伽马分布的特征及模拟性质;通过已知可识最小值及差值的分布密度,所有参数皆可识别,得到识别性质;通过计算X,Y之间的相关系数,证明了相关系数落在(0,1)内,得到相关性质,证明了X的尾部关于Y的尾部渐近不相关以及Y的尾部关于X的尾部渐近正相关,得到渐近性质;最后,得到了四参数二元McKay型伽马分布参数的矩估计及最大似然估计.从应用层面考虑,采用二步拟合,先导出了位置参数的最大似然估计,进而导出尺度参数和形态参数的矩估计,得到估计性质.利用已有文献中的实例数据,给出了基于四参数二元McKay型伽马分布的地震灾害评估参数的估计值.

Some properties of the four-parameter McKay’s bivariate gamma distribution are considered in this paper.By using the technique of variate substitution,the characterization of the McKay’s bivariate gamma distribution are derived,from which an efficient simulation of the McKay’s bivariate gamma distribution is obtained.Also if the joint distribution of identified minimum and differential value is known,then all of parameters are identified;and correlation coefficient of X and Y is calculated.It is proven that the value of correlation coefficient is between zero and one;it also shows that the tail of X with respect to the tail of Y is asymptotically independent,while the tail of Y with respect to the tail of X is asymptotically positive related.The moment estimators and maximum likelihood estimators of parameters of the four-parameter McKay’s gamma distribution are obtained.Finally,taking into account the application,fitting data by way of two steps,the moment estimator of one parameter,the maximum likelihood estimator of another parameter,as well as themodified moment estimators of the other two parameter of the four-parameter McKay’s bivariate gamma distribution are derived based on integrating the method of moment estimator with the method of maximum likelihood estimator.In the end,the results of fitting to the earthquake data from the reference are provided.