标题： 一种用于威布尔分布参数的新估计器：威布尔分布的全面比较研究 显示英文标题

标题： A new estimator for Weibull distribution parameters: Comprehensive comparative study for Weibull Distribution

摘要： 威布尔分布已在工程和科学领域得到了广泛的应用。估计量的效用和实用性高度取决于实践者的研究领域。在实际中，用户在不同参数设置和样本大小下寻找他们所需的估计量。在本文中，我们关注两个主题。首先，我们提出了用于威布尔分布参数的$U$统计量。所提出的$U$统计量的一致性和渐近正态性通过理论和模拟得到了证明。文献中已经提出了几种估计威布尔分布参数的方法。这些方法包括：广义最小二乘类型1，广义最小二乘类型2，$L$矩，对数矩，最大似然估计，矩法，分位数法，加权最小二乘法和加权最大似然估计。其次，由于缺乏对威布尔分布参数估计量的全面比较，我们对所提出的$U$统计量和上述九种估计量进行了全面的比较研究。根据模拟结果，当样本量较大时，我们提出的$U$统计量在估计形状和尺度参数的偏差方面表现出最佳性能。 显示英文摘要

摘要： Weibull distribution has received a wide range of applications in engineering and science. The utility and usefulness of an estimator is highly subject to the field of practitioner's study. In practice users looking for their desired estimator under different setting of parameters and sample sizes. In this paper we focus on two topics. Firstly, we propose $U$-statistics for the Weibull distribution parameters. The consistency and asymptotically normality of the introduced $U$-statistics are proved theoretically and by simulations. Several of methods have been proposed for estimating the parameters of Weibull distribution in the literature. These methods include: the generalized least square type 1, the generalized least square type 2, the $L$-moments, the Logarithmic moments, the maximum likelihood estimation, the method of moments, the percentile method, the weighted least square, and weighted maximum likelihood estimation. Secondary, due to lack of a comprehensive comparison between the Weibull distribution parameters estimators, a comprehensive comparison study is made between our proposed $U$-statistics and above nine estimators. Based on simulations, it turns out that the our proposed $U$-statistics show the best performance in terms of bias for estimating the shape and scale parameters when the sample size is large.