三参数Ⅰ型广义Logistic分布参数的一类改进估计

An Improved Estimation for 3-parameter Type ⅠGeneralized Logistic Distribution

广义Logistic分布族在生物、医学、金融管理,以及气象、水文、地质等领域有重要的应用。迄今为止,对此分布族的研究已取得了一系列重要成果;令人遗憾的是,关于三参数I型广义Logistic分布的研究还很不深入。本文利用矩法首先讨论三参数I型广义Logistic分布形状参数的估计,然后利用线性回归分析方法讨论分布的位置参数和刻度参数的估计,改进矩估计。本文所给出的分布参数的估计方法简单、有效;证明了在一定的条件下,本文给出的估计量存在、唯一,且模拟显示:估计量在中小样本情形下,一致优于分布参数的矩估计和L矩估计;特别是在样本容量n介于20和30之间时,估计量有更小的估计偏差和方差。估计方法简单、实用且有效。

There are many important applications in biology, medicine, financial management, meteorology, hydrology, geology and other fields for the generalized Logistic distributions. So far, a series of important achievements have been obtained for this family distributions. Unfortunately, the 3-parameter type I generalized Logistic distribution needs further research. We using moment method to discussed the shape parameter estimation. And then, using linear regression model to discussed location parameter and scale parameter estimation, improved the moment estimates. We proposed the parameter estimation method is simple and effective. We proved that estimates exist and the only, under certain conditions. Simulation research shows that： We proposed the estimates are always better than moment estimates and L-moment estimates, in the case sample size is small or medium. In particular, when the sample size n between 20 to 30, the estimators have smaller bias and variance.