基于矩和L矩的三参数Ⅰ型广义Logistic分布的参数估计  

Parameter Estimations for 3-parameter Type Ⅰ Generalized Logistic Distribution by Methods of Moments and L-moments

作　　者：韩雪[1] 程维虎[2] 

机构地区：[1]济南大学数学科学学院,济南250022 [2]北京工业大学应用数理学院,北京100124

出　　处：《应用数学学报》2017年第3期331-344,共14页Acta Mathematicae Applicatae Sinica

基　　金：国家统计局科研(2015LY86);山东省自然科学基金(ZR2016AM01);济南大学科研基金(XKY1612)资助项目

摘　　要：广义Logistic分布是一族重要的分布,被广泛地应用于生物学、医学、金融管理学,以及气象、水文、地质等领域.迄今为止,对于Logistic分布,统计学者已给出诸多的统计推断理论和方法,以及众多应用成果.令人遗憾的是,对应用非常广泛的广义Logistic分布,特别是具有位置、刻度和形状参数的三参数Ⅰ型广义Logistic分布的研究还有待深入,该分布的应用还需进—步开发和利用.本文利用矩法和L矩法讨论三参数Ⅰ型广义Logistic分布的参数估计,给出两种估计形式下参数的估计方程;证明了在一定的条件下,估计方程的解存在、唯一,且渐近正态地相合于真实参数的结论.通过计算机模拟,比较不同参数、不同样本容量下两种估计的估计效果.The generalized Logistic distribution is an important distribution, and widely used in biology, medicine, financial management, meteorology, hydrology, geology and other fields. So far, many statistical scholars have proposed many theories and methods of statis- tical inference, and a wide range of applications for the Logistic distribution. Unfortunately, the Logistic distribution, especially the type I generalized Logistic distribution with location- scale-shape parameter, needs further research, tile application of this distribution needs more exploration and exploitation. We discussed the parameter estimations for 3-parameter type I generalized Logistic distribution using methods of moments and L moments, provided two parameter estimate equations, proved the existence, uniqueness and asymptotically normal consistency of the solution of the estimate equations under some conditions in this paper. We compared the estimated results about the two parameter estimations, in cases of different parameters, different sample size by simulation.

关 键 词：I型广义Logistic分布 矩估计 L矩估计 渐近正态性 相合性 计算机模拟 

分 类 号：O212.1[理学—概率论与数理统计]