一类折叠Gamma分布的尖峰厚尾性质及应用  

Sharp Peak and Fat Tail Property of a Type of Folded Gamma Distribution and Its Application

作　　者：陈明光 王源昌[1] Chen Mingguang;Wang Yuanchang(School of Mathematics,Yunnan Normal University,Kunming 650500,China)

机构地区：[1]云南师范大学数学学院,昆明650500

出　　处：《统计与决策》2024年第8期28-33,共6页Statistics & Decision

基　　金：国家自然科学基金资助项目(71163046);国家社会科学基金资助项目(16ZDA041);云南省自然科学基金资助项目(2018RD004)。

摘　　要：组合分布思想的出现及扩展为研究现实数据分布提供了优良方案。鉴于许多数据的尖峰后尾特征,文章从Gamma分布出发,构造了具有尖峰厚尾性质的折叠Gamma分布,进而讨论了折叠Gamma分布的性质,并在Newton-Raphson算法下给出了分布参数的矩估计和极大似然估计,同时以数值模拟证明了估计的可行性,最后以实际数据对比研究折叠Gamma分布和正态分布的拟合效果。结果表明:折叠Gamma分布能更好地拟合尖峰厚尾数据,且其拟合效果随着数据样本量的增大而变好。The emergence and expansion of the idea of combinatorial distribution provide an excellent scheme for studying the distribution of realistic data.In view of sharp peak and fat tail property of many data,this paper constructs a folded Gamma distribution with sharp peak and fat tail properties from the Gamma distribution,discusses the nature of the folded Gamma distri-bution,and gives the moment estimation and maximum likelihood estimation of the distribution parameters under the New-ton-Raphson algorithm.Finally,the paper proves the feasibility of the estimation by numerical simulation,and also studies the fit-ting effect of the folded Gamma distribution and the normal distribution by comparing the actual data.The results show that the folded Gamma distribution can better fit the sharp peak and fat tailed data,and that the fitting effect is better with the increase of the data sample size.

关 键 词：折叠Gamma分布 尖峰厚尾 GAMMA分布 金融收益率 

分 类 号：O212.2[理学—概率论与数理统计]