非对称三参数Student-t分布的参数估计及应用  

Parameter Estimation and Application of Asymmetric Three-parameter Student-t Distribution

作　　者：郝家岗 钱夕元[1] Hao Jiagang;Qian Xiyuan(School of Science,East China University of Science and Technology,Shanghai 200237,China)

机构地区：[1]华东理工大学理学院,上海200237

出　　处：《统计与决策》2021年第11期25-29,共5页Statistics & Decision

基　　金：国家高科技研究发展计划(“863计划”)资助项目(2015AA20107)。

摘　　要：文章基于t分布构造了一个新的非对称三参数Student-t分布。推导了新分布的累计分布函数、分位数函数、随机变量表达式和原点矩估计等基础性质,使用了矩方法、极大似然估计法和贝叶斯估计法等进行了参数估计,并通过生成模拟数据的方法比较验证了三种方法的合理性。最后,将新分布代入实例中拟合,结果表明新分布相比其他的分布,在非对称和厚尾方面具有更好的拟合能力。This paper constructs a new asymmetric three-parameter Student-t distribution based on t distribution, deduces the basic properties of the new distribution, such as the cumulative distribution function, the quantile function, the expression of random variable and the estimation of the origin moment, and uses the moment method, maximum likelihood estimation method and Bayesian estimation method to estimate the parameters. Then, the paper compares and verifies the rationality of the three methods by generating simulation data. Finally, the paper substitutes the new distribution into the example for fitting, and the results show that the new distribution has better fitting ability than other distributions in terms of asymmetry and fat tail.

关 键 词：偏态厚尾 非对称Student-t分布 贝叶斯估计 数据拟合 

分 类 号：O21[理学—概率论与数理统计]