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 基于序统计量 Extropy的检验分布对称性的新方法

张虹1,邱国新1,2   

  1. 1. 安徽新华学院商学院, 合肥 230088; 2. 中国科学技术 大学管理学院, 合肥 230026
  • 出版日期:2021-02-25 发布日期:2021-04-19

张虹,邱国新.  基于序统计量 Extropy的检验分布对称性的新方法[J]. 系统科学与数学, 2021, 41(2): 577-588.

ZHANG Hong, QIU Guoxin. Testing Symmetry Based on the Extropy of Order Statistics[J]. Journal of Systems Science and Mathematical Sciences, 2021, 41(2): 577-588.

Testing Symmetry Based on the Extropy of Order Statistics

ZHANG Hong1 ,QIU Guoxin 1,2   

  1. 1. School of Business, Xinhua University of Anhui, Hefei 230088; 2. School of Management, University of Science and Technology of China, Hefei 230026
  • Online:2021-02-25 Published:2021-04-19

包括夏普-林特纳资本资产定价模型和布莱克-斯科尔斯期权定价模型在内的很多模型, 都离不开分布对称性假设. 因此, 应用这些模型前必须认真检验 对称性假设是否成立.文章基于(Qiu, 2017)中的一个定理以及序统计量的 Extropy, 提出了检验分布对称性的一种新方法. 与已有检验方法相比, 这种新的检验方法不需要知道未知分布的对称中心, 而且蒙特卡罗模拟显示, 该方法比已有检验方法具有更好的检验势.最后, 给出一个实例以说明新检验方法的实际效果.

Symmetry is an implicit or explicit assumption in some widely used models, including the Sharpe-Lintner capital asset pricing model and the Black-Scholes option pricing model. Therefore, we must check carefully the symmetry assumption before using these models. Based on a theorem obtained in (Qiu, 2017) and the extropy of order statistics, we propose a new test statistic for testing symmetry of the continuous distribution in this paper. Our new test has an advantage that we do not need to estimate the center of the symmetry. Moreover, for a great variety of alternative asymmetric distributions, Monte Carlo simulation shows that our proposed test performs well by comparing its powers with that of other tests for symmetry. Finally, a real data set is used to illustrate the performance of our proposed test.

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