Estimation of Parameters in the Weibull Distribution

A new method of estimation is used to obtain two simple estimators of the parameters in a Weibull distribution. These estimators are similar to the estimators given by Gumbel, Miller and Freund, and Menon. Some useful properties of these estimators are developed which make it practical to use Monte Carlo methods to determine the variances and biases of the estimators for various sample sizes. Comparisons of the estimators can be made and unbiasing factors calculated in some cases. The variances of the estimators are also compared to the Cramer-Rao lower bounds for regular unbiased estimators.