Abstract
This paper attempts to identify the best method of estimating the parameters of the two-parameter Weibull distribution using data from complete samples. Various methods of estimating the Weibull parameters have been proposed, but adequate criteria in user side to judge which method is the optimum have not been developed. In several papers comparing the biases and expected losses in the estimators of the Type I extreme value distribution has been used. However, the two parameters are simultaneously estimated from a sample, not one by one separately, and they are used in the Weibull distribution. This paper uses the concepts of the Kolmogorov-Smirnov and chi-square goodness-of-fit tests, as well as biases and expected losses of estimators in the Weibull and Type I extreme value distributions, as criteria to select an appropriate method. Monte Carlo simulation provides sets of 2000 complete samples for each combination of sample sizes n=3, 6, 10, and 20, and shape parameters β=0.5, 1, 3, and 10. The eight methods of three kinds of graphical plotting techniques, two kinds of moments methods, maximum-likelihood estimation, and two kinds of linear estimation techniques are compared. This investigation concludes the best linear unbiased estimators (BLUE) to be the best among the eight methods for general use and recommends median ranks for probability plotting.
