Quantile第Ⅰ类分布的参数估计及假设检验

发布时间：2018-06-23 05:47

本文选题：极大似然估计 + 大样本性质　；参考：《海南师范大学》2017年硕士论文

【摘要】：Quantile第Ⅰ类分布是一类为克服经典分布在拟合金融收益率数据表现不佳而提出来的新分布族,其拥有的可变尾部厚度、独立变化的左右尾厚度及显示的分位数函数的特征,使其在拟合金融数据时明显优于诸如正态分布,stable分布等经典分布.自其提出以来,已成功应用于国内外证券市场、外汇市场、美国电力市场价格市场,以及流体力学中的湍流等的实证研究.然而,其参数估计,假设检验等重要的工作尚未有系统的研究工作出现.本文主要研究了 Quantile第Ⅰ类分布的极大似然估计(MLE)的大样本性质,成功证明了其参数的MLE的相合性和渐进正态性.并通过应用中心极限定理给出了此三个参数的假设检验及置信区间估计的理论结果.最后,用matlab软件进行了数值模拟.当参数μ已知时,Quan-tile第Ⅰ类分布的其它三个参数的MLEs结果非常好;当位置参数μ未知时,Quantile第Ⅰ类分布的四个参数的MLEs结果在样本量很大的情况下也非常好.
[Abstract]:Quantile Class I distribution is a new distribution family proposed to overcome the poor performance of classical distribution in fitting financial yield data. It has the characteristics of variable tail thickness, independent left and right tail thickness and displayed quantile function. It is better than classical distribution such as normal distribution and stable distribution in fitting financial data. Since it was proposed, it has been successfully applied to the empirical studies of domestic and foreign stock markets, foreign exchange markets, American electricity market price markets, and turbulence in fluid dynamics. However, some important work, such as parameter estimation and hypothesis test, have not been systematically studied. In this paper, we study the large sample properties of maximum likelihood estimation (MLE) of Quantile class I distribution, and prove the consistency and asymptotic normality of MLE of its parameters. The hypothesis test of these three parameters and the theoretical results of confidence interval estimation are given by applying the central limit theorem. Finally, numerical simulation is carried out with matlab software. When the parameter 渭 is known, the MLEs results of the other three parameters of Quantile class I distribution are very good, and the MLEs results of the four parameters of the Quantile class I distribution are also very good when the position parameter 渭 is unknown.
【学位授予单位】：海南师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.1

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