Engeman R M, Keefe T J
Comput Biomed Res. 1985 Aug;18(4):391-6. doi: 10.1016/0010-4809(85)90017-5.
An efficient two-step method of estimating the scale parameter of the Weibull distribution is presented and compared to other estimation procedures. The shape parameter is obtained by a procedure other than maximum likelihood and then substituted into the maximum likelihood formula for the scale parameter. Three two-step and four one-step estimators were compared using a Monte Carlo simulation. When the shape parameter is less than one, the two-step estimator using a generalized least-squares estimate of the shape parameter was best in terms of observed relative efficiency. Maximum likelihood was best, but followed closely by the generalized least-squares estimator when the shape parameter is greater than one.
提出了一种有效的两步法来估计威布尔分布的尺度参数，并将其与其他估计方法进行比较。形状参数通过最大似然法以外的方法获得，然后代入尺度参数的最大似然公式中。使用蒙特卡罗模拟比较了三个两步估计器和四个一步估计器。当形状参数小于1时，就观察到的相对效率而言，使用形状参数广义最小二乘估计的两步估计器是最好的。当形状参数大于1时，最大似然估计器是最好的，但广义最小二乘估计器紧随其后。
