三维power-normal分布的性质及参数估计问题的研究

Research on the Properties and Parameter Estimation Problem of Three-dimensional Power-normal Distribution

应用了Clayton连接函数的性质给出了三维power-normal分布的分布函数及概率密度函数,并详细研究了三维power-normal分布的基本性质,同时,根据所构造出的三维power-normal分布模型,对其中的参数进行了最大似然估计的讨论。并给出了参数的最大似然估计的算法。结合费永法在文献中的1964年到1973年10年间长江大通站、淮河中渡站及黄河花园口站的天然年流经量数据作为样本数据,利用MATLAB程序计算了参数的最大似然估计。

In this paper, the cumulative distribution function and probability density function of three-dimensional power-normal distribution are given by using the properties of Clayton copula function. The basic properties of power-normal distribution are investigated in detail. At the same time, the maximum likelihood estimation of the parameters are discussed according to the three-dimensional power-normal distribution model. According to Fei Yongfa, who mentioned in the article, from 1964 to 1973 the annual flows data as the sample data among Datong station in the Yangtze River and the Huaihe River Ferry station and Huayuankou Station of the Yellow River, we use the MATLAB language to calculate the parameters of maximum likelihood estimation.