| 广义Pareto分布的参数估计 |
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| 引用本文： | 马彦伟,赵彬宇,谢建国,孙光霞.广义Pareto分布的参数估计[J].贵州教育学院学报,2014(6):5-8. |
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| 作者姓名： | 马彦伟 赵彬宇 谢建国 孙光霞 |
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| 作者单位： | 贵州师范学院数学与计算机科学学院,贵州贵阳550018 |
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| 基金项目： | 贵州师范学院大学生科研项目：广义Pareto分布参数估计（12YB0021）. |
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| 摘 要： | 广义Pareto分布(Generalized Pareto Distribution,简称GPD)是统计推断中重要的一个分布,其目前在诸多领域得到广泛的应用.GPD的参数估计方法有多种,但各种方法及估计效果一般都受到形状参数k的限制,总结几种常用的参数估计方法,如:矩估计(the method of moments,简记MOM)、最小二乘估计(the least squares estimation,简记LSE)、基于分位数估计(the elemental percentile method,简记EPM)、近似广义最小二乘估计(AGLSE)等,通过模拟研究,得出不存在一致最优的参数估计方法.而在k较大时,LSE在GPD参数估计中模拟效果较为理想,特别当k1/2时,AGLSE对k的估计精度较高.
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| 关 键 词： | 广义Pareto分布 GPD参数估计 最小二乘估计 |
Parameter estimation of generalized Pareto distribution |
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| MA Yan-wei,ZHAO Bin-yu,XIE Jian-guo,SUN Guang-xia.Parameter estimation of generalized Pareto distribution[J].Journal of Guizhou Educational College(Social Science Edition),2014(6):5-8. |
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| Authors: | MA Yan-wei ZHAO Bin-yu XIE Jian-guo SUN Guang-xia |
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| Institution: | (School of Mathematics and Computer Science, Guizhou Normal College, Guiyang, Guizhou, 550018) |
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| Abstract: | The generalized Pareto distribution （ GPD）, one of important distributions of statistical inference, is widely used in many fields. There are a great variety of methods for estimating the parameters of the GPD, but all methods and estimated effect are generally confined to parameter k. This paper summarizes several common methods of parameter estimation, including the method of moments （ MOM）, the least squares estimation （ LSE）, the elemental percentile method （EPM）, and the approximate generalized least squares estimation （AGLSE）etc. Through the simulation study, it is concluded that there is no consistent optimal parameter estimation method. But when k is bigger, the simulation effect of the LSE in the parameter estimation of GPD is more ideal, especially when I k l 〈 1/2, AGLSE＇s estimation of k is more precise. |
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| Keywords: | generalized Pareto distribution parameter estimation of GPD the least squares estimators |
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