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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, 上海 201620
摘要:
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的两种矩估计和极大似然估计,并通过Monte-Carlo模拟考察了估计的精度.最后选取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分布对中国股市大盘进行实证分析,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的日收益率,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
DOI:10.3969/J.ISSN.1000-5137.2018.01.002
分类号:
基金项目:国家自然科学基金(11671264)
The statistical analysis and application of asymmetric three-parameter weibull distribution
Hu Yinhua, Xu Xiaoling
School of Statistics and Information, Shanghai University of International Business and Economics, Shanghai 201620, China
Abstract:
On the basis of two-parameter Weibull distribution,we propose asymmetric three-parameter Weibull distribution which takes values in (-∞,+∞),and study its graphic features of the density function as well as the numerical characteristics of this distribution. In the full sample cases,we offer two moment estimation methods and MLE method to estimate the parameters of the distribution,and study the accuracy of our estimation by using the Monte-Carlo simulation.We choose data of Shanghai Composite Index and Shenzhen Component Index from Jan.4th,2016 to May 6th,2016,and apply the asymmetric three-parameter Weibull distribution model to carry out the empirical analysis on these two market indices of China.We show that the asymmetric three-parameter Weibull distribution model fits well the daily return of Chinese stock market index,and also get the point estimation for relevant parameters at the same time.
Key words:  asymmetric three-parameter Weibull distribution  shape parameter  scale parameter  moment estimation  MLE  index return  KS test