文献类型：期刊文献

中文题名：非对称三参数广义误差分布的参数估计及应用

英文题名：Parameters Estimation and Application for the Asymmetric 3-Parameter Generalized Error Distribution

作者：张文清[1];钱夕元[1]

机构：[1]华东理工大学数学学院,上海200237

年份：2022

卷号：48

期号：3

起止页码：411

中文期刊名：华东理工大学学报（自然科学版）

外文期刊名：Journal of East China University of Science and Technology

收录：Scopus;北大核心:【北大核心2020】；CSCD:【CSCD_E2021_2022】；

基金：国家高技术研究发展计划(“863计划”)资助项目(2015AA20107)。

语种：中文

中文关键词：非对称广义误差分布;非对称数据;尖峰厚尾;贝叶斯推断

外文关键词：asymmetric generalized error distribution;asymmetric data;leptokurtosis&fat-tail;Bayesian inference

摘要：针对实际数据的尖峰厚尾和非对称特性,通过在广义误差分布中加入偏度参数,同时分别引入两个参数控制左尾和右尾,构造了一个新的非对称三参数广义误差分布。本文首先研究了该分布的基本性质,包括累积分布函数、分位数函数及各阶原点矩等,并给出了随机变量的抽样方法;其次分别给出了用矩估计、极大似然方法和贝叶斯估计法来估计该分布参数的步骤,并通过马尔科夫链蒙特卡罗方法生成的模拟数据验证比较了这3种方法;最后将该分布应用于两组实际数据中,利用非对称三参数广义误差分布对尖峰厚尾非对称的数据进行拟合。
To fit the data with leptokurtosis and fat tail, a new asymmetric generalized error distribution model is proposed by introducing a skewness parameter to the generalized error distribution, and using two tail parameters to control the left tail and right tail, respectively. This model can flexibly fit asymmetric and fat-tailed data sets. Firstly,the basic properties of the model are discussed in detail, including the cumulative distribution function, the quantile function, the origin moment of each order and so on, and the sampling method of the random variable is given.Secondly, the procedure to estimate the parameters of the model with moment estimation, maximum likelihood method and Bayesian method are discussed respectively, and these three methods are compared by the simulated data generated by Markov Monte Carlo method. Finally, two applications to real data sets are reported to illustrate the performance of this new asymmetric generalized error distribution in fitting the data with leptokurtosis and asymmetry.