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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), 2022, 48(3): 411-418. 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), 2022, 48(3): 411-418. 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, 2022, 48(3): 411-418. 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, 2022, 48(3): 411-418. 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-),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。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。

     

  • 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  3种方法参数的估计结果

    Figure  2.  Parameter estimation results of three methods

    图  3  经验累积分布函数和拟合的AGED模型累积分布函数比较

    Figure  3.  CDF comparision of empirical model and 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.  CDF comparision of empirical model and 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

    TypesMeanStandard
    deviation
    SkewnessKurtosisMinMax
    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

    TypesMeanStandard
    deviation
    SkewnessKurtosisMinMax
    Raw
    data
    0.89 0.35 −1.51 2.3 −0.4 1.36
    Transformed
    data
    −0.42 0.71 −1.51 2.3 −3.0 0.52
    下载: 导出CSV
  • [1] SUBBOTIN M T. On the law of frequency of error[J]. Matematicheskii Sbornik, 1923, 31(2): 296-301.
    [2] BOX G E P, TIAO G C. A further look at robustness via Bayes's theorem[J]. Biometrika, 1962, 49: 419-432. doi: 10.1093/biomet/49.3-4.419
    [3] NELSON D B. Conditional heteroskedasticity in asset returns: A new approach[J]. Econometrica, 1991, 59: 347-370. doi: 10.2307/2938260
    [4] HSIEH D A. Modeling heteroskedasticity in daily foreign exchange rates[J]. Journal of Business and Economics Statistics, 1989, 7: 307-317.
    [5] MCDONALD J B, NEWEY W K. Partially adaptive estimation of regression models via the generalized t distribution[J]. Econometric Theory, 1988, 4: 428-457. doi: 10.1017/S0266466600013384
    [6] THEODOSSIOU P. Financial data and the skewed generalized t distribution[J]. Management Science, 1998, 44(12/1): 1650-1661.
    [7] CAPPUCCIO N, LUBIAN D, RAGGI D. MCMC Bayesian estimation of a skew-GED stochastic volatility model[J]. Studies in Nonlinear Dynamics & Econometrics, 2007, 8(2): 1-31.
    [8] ANDERSON D. Algorithms for minimization without derivatives[J]. Transactions on Automatic Control, 1974, 19: 632-633. doi: 10.1109/TAC.1974.1100629
    [9] SURHONE L M, TIMPLEDON M T, MARSEKEN S F, et al. Newton's method[J]. Siam Journal on Numerical Analysis, 2010, 35(1/3): 207-215.
    [10] SIBUYA M. Generalized hypergeometric, digamma and trigamma distributions[J]. Annals of the Institute of Statistical Mathematics, 1979, 31(3): 373-390. doi: 10.1007/BF02480295
    [11] CHRISTIAN R, JEAN M M. Bayesian Core: A Practical Approach to Computational Bayesian Statistics[M]. New York: Springer-Verlag, 2007.
    [12] WOLPERT R L. A conversation with James O. Berger[J]. Statistical Science, 2004, 19(1): 205-218.
    [13] BARROS M, GALEA M, GONZÁLEZ M, et al. Influence diagnostics in the tobit censored response model[J]. Statistical Methods & Applications, 2010, 19: 379-397.
    [14] TOVAR-FALÓN R, BOLFARINE H, MARTÍNEZ-FLÓREZ G. The asymmetric alpha-power skew-t distribution[J]. Symmetry, 2020, 12(1): 82. doi: 10.3390/sym12010082
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出版历程
  • 收稿日期:  2021-03-08
  • 网络出版日期:  2021-06-24
  • 刊出日期:  2022-06-29

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