基于矩和L矩的三参数Ⅰ型广义Logistic分布的参数估计

发布时间：2018-06-14 15:37

本文选题：Ⅰ型广义Logistic分布 + 矩估计　；参考：《应用数学学报》2017年03期

【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.
[Abstract]:Generalized Logistic distribution is a family of important distribution, which is widely used in biology, medicine, financial management, meteorology, hydrology, geology and other fields. So far, for Logistic distribution, statisticians have given a lot of statistical inference theories and methods, as well as a lot of application results. It is regrettable that the research on the generalized Logistic distribution, especially the three-parameter generalized logistic distribution with location, scale and shape parameters, needs to be further studied, and its application needs to be further developed and utilized. In this paper, we discuss the parameter estimation of three parameter generalized Logistic distribution by using the moment method and L moment method, give the parameter estimation equations in two kinds of estimation forms, and prove that under certain conditions, the solution of the estimation equation is unique. And asymptotically normality coincides with the conclusion of real parameters. By computer simulation, the estimation effects of two kinds of estimators with different parameters and different sample sizes are compared.
【作者单位】：济南大学数学科学学院;北京工业大学应用数理学院;
【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
【分类号】：O212.1

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