威布尔分布参数估计新方法研究

由样本估计威布尔分布的三个参数是工程中的一个重要问题。应用改进的一阶灰色微分方程模型直接建模方法，可以导出不经迭代就估计出威布尔分布三个参数的灰色估计方法。用这种方法估计参数先得到形状参数，不用迭代，简单明了。实际数据计算和大量的蒙特卡洛模拟试验表明，对形状参数大于1的分布，拟合优度好，精度较高。

NEW ESTIMATION METHOD OF THREE-PARAMETER WEIBULL DISTRIBUTION

Weibull distribution is an extraordinary important distribution in reliability engineering. In this paper, a new estimation method for the three parameters of Weibull distribution that hasn't iteration process was introduced based on the first order grey linear differential equation of Grey model, the shape parameter was obtained first, then the location parameter and the characteristic parameter are estimated by using the method of least square regression. The digital simulation has shown that the present approach is simpler and the estimating accuracy is better when the shape parameter is greater than 1. Thus, the practicability of the method has been proved.