三参数Ⅰ型广义Logistic分布参数的改进最小二乘估计

An Improved Least Squares Estimators for Three-Parameter Type Ⅰ Generalized Logistic Distribution

广义Logistic分布在工业、生物、地质、水文等领域有着广泛的应用。本文针对三参数的广义Logistic分布,提出了基于Logistic变换下参数的最小二乘估计,并给出了参数估计的收敛速度。通过Monte-Carlo模拟对提出的估计方法和已有方法进行比较,结果表明：所给的估计量具有更好的估计效果。最后通过单位长度碳素纤维的硬度数据进一步说明了所提出的估计方法的可行性。

The generalized logistic distribution is widely used in the fields of industry, biology, geology,hydrology and so on. In this paper, we propose a least squares estimator based on Logistic transformation for three-parameter type Ⅰ generalized logistic distribution. Some asymptotic results are provided.A simulation is undertaken to assess the performance of the proposed method and to compare them with other methods suggested in this paper. The simulation results indicate that the proposed method performs better than some other methods. Finally, the proposed method is applied to a strength data for single carbon fibers.