Research On Multidimensional Power-normal Distribution And Its Parameter Estimation

When studying the multi-dimensional distribution, we need to consider the correlation problem. Using the copula function to describe the correlation structure between variables, we do not need to calculate the same marginal distribution every time, and the joint distribution of any marginal can be constructed by the copula function. Therefore, many scholars at home and abroad put forward the application of copula function to research the multi-dimensional distribution. In this paper, based on the theory of copula function and the skewed normal distribution, we discuss the basic properties and parameter estimation of multi-dimensional power-normal distribution by using copula function, and based on the two power-normal distribution of the Gupta and Kundu two scholars, extend two power-normal distribution to the p-dimension distribution.First of all, based on the above research theory, this paper makes a further study on the definition and properties of power-normal distribution and two power-normal distribution. We use MATLAB program to estimate the maximum likelihood estimate of the parameters of two power-normal distribution, and compared with the existing two methods of maximum likelihood estimate(direct likelihood estimate and two-step process).Secondly, the article focuses on the three-dimension power-normal distribution, because Clayton copula is a simple and highly relevant copula, based on the properties of three-dimension Clayton copula, we can obtain the distribution and the probability density function of three-dimension power-normal distribution by use of the properties of Clayton copula and the method of variable. And give its basic properties and proof process. At the same time, using the maximum likelihood estimation method to estimate the unknown parameter? of Clayton copula and the unknown parameters1 2 3?, ?, ? of the power-normal distribution, and give the specific parameters estimation by the MATLAB language.Finally, through the study of the distribution and properties of the lower dimension power-normal distribution, the joint distribution function and probability density function of p-dimension power-normal distribution are derived, and provide the basic properties and the likelihood estimation equation for the parameter estimation of p-dimension power-normal distribution.