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  • ISSN 1006-3080
  • CN 31-1691/TQ

非对称三参数广义误差分布的参数估计及应用

张文清 钱夕元

张文清, 钱夕元. 非对称三参数广义误差分布的参数估计及应用[J]. 华东理工大学学报(自然科学版). doi: 10.14135/j.cnki.1006-3080.20210308001
引用本文: 张文清, 钱夕元. 非对称三参数广义误差分布的参数估计及应用[J]. 华东理工大学学报(自然科学版). doi: 10.14135/j.cnki.1006-3080.20210308001
ZHANG Wenqing, QIAN Xiyuan. Parameters Estimation and Application for the Asymmetric 3-Parameter Generalized Error Distribution[J]. Journal of East China University of Science and Technology. doi: 10.14135/j.cnki.1006-3080.20210308001
Citation: ZHANG Wenqing, QIAN Xiyuan. Parameters Estimation and Application for the Asymmetric 3-Parameter Generalized Error Distribution[J]. Journal of East China University of Science and Technology. doi: 10.14135/j.cnki.1006-3080.20210308001

非对称三参数广义误差分布的参数估计及应用

doi: 10.14135/j.cnki.1006-3080.20210308001
基金项目: 国家高技术研究发展计划(“863计划”)资助项目(2015AA20107)
详细信息
    作者简介:

    张文清(1996.3-),女,江苏淮安人,硕士生,主要研究方向为统计计算。E-mail:13127990978@163.com

    通讯作者:

    钱夕元,E-mail:xyqian@ecust.edu.cn

  • 中图分类号: O213

Parameters Estimation and Application for the Asymmetric 3-Parameter Generalized Error Distribution

  • 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。该分布在拟合对称性和尾部方面有更大的灵活性,便于拟合非对称和尖峰厚尾数据。本文详细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,并通过马尔科夫蒙特卡罗方法生成的模拟数据验证比较了这三种方法;最后将该分布应用于两组实际数据中,来阐述非对称三参数广义误差分布拟合尖峰厚尾非对称数据方面的表现。

     

  • 图  1  不同参数取值下AGED的概率密度函数曲线

    Figure  1.  Probability distribution function curve of AGED with different parameter values

    图  2  三种方法参数估计结果

    Figure  2.  Parameter estimation results of three methods

    图  3  经验累积分布函数和拟合的AGED模型累积分布函数图

    Figure  3.  Empirical CDF and CDF of fitted AGED model

    图  4  火山高度数据拟合曲线

    Figure  4.  Fitting curve for the volcano height data

    图  5  经验累积分布函数和拟合的AGED模型累积分布函数图

    Figure  5.  Empirical CDF and CDF of fitted AGED model

    图  6  恒星丰度数据拟合曲线

    Figure  6.  Fitting curve for the stellar abundances data

    表  1  火山高度数据的描述统计量

    Table  1.   Descriptive statistics for the volcano height data

    MeanStandard deviationSkewnessKurtosisMinMax
    Raw data1694.171591.350.491.57-57006879
    Transformed data0.260.530.491.57-2.21.99
    下载: 导出CSV

    表  2  恒星丰度数据的描述统计量

    Table  2.   Descriptive statistics for the stellar abundances data

    MeanStandard
    deviation
    SkewnessKurtosisMinMax
    Raw data0.890.35−1.512.3−0.41.36
    Transformed data−0.420.71−1.512.3−30.52
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-03-08
  • 网络出版日期:  2021-06-24

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