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非对称三参数Weibull分布的统计分析及其应用
胡银花, 徐晓岭
上海对外经贸大学统计与信息学院,201620
摘要:
本文在两参数Weibull分布的基础上,提出了一种取值于上的非对称三参数Weibull分布,研究了其密度函数的图形特征,给出了该分布的数字特征,在全样本场合下给出了参数两种矩估计和极大似然估计,通过Monte-Carlo模拟考察了估计的精度。论文最后选取了2016年1月4日至2016年5月6日上证综指和深圳成指的数据,应用非对称三参数Weibull分布对中国大盘股市进行实证分析,结果表明非对称三参数Weibull分布模型能够较好地拟合中国股市大盘日收益率,同时还得到了相应参数的点估计。
关键词:  非对称三参数Weibull分布,形状参数,刻度参数,矩估计,极大似然估计,股指收益率,KS检验
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基金项目:国家自然科学基金项目(面上项目,重点项目,重大项目)
The Statistical Analysis and Application of Asymmetric Three-parameter Weibull Distribution
Yinhua Hu, Xiaoling Xu
Shanghai University of International Business and Economics,School of Statistics and Information
Abstract:
On the basis of Weibull distribution, this article puts forward the asymmetric three- parameter Weibull distribution whose values in , and studies its graphic features of the density function as well as the numerical characteristics of this distribution. Furthermore, under the full sample cases, this paper also offers two moment estimation methods and LME to estimate the parameters of the distribution, and studies the estimated?accuracy by using the Monte-Carlo simulation. This paper chooses data of shanghai composite index and shenzhen component index during Jan. 4th, 2016 to May 6th, 2016, and then apply the asymmetric three-parameter Weibull distribution model to have an empirical analysis on the broad market of Chinese. The result turns out that the asymmetric three- parameter Weibull distribution model can well present the distribution of the daily return of Chinese broad market and we get the point estimation for relevant parameters at the same time.
Key words:  Asymmetric  Three-parameter  Weibull Distribution, Shape  Parameter, SScale  Parameter, Moment  Estimation, MLE, Index  Return, KS  Test