On estimating Weibull modulus by moments and maximum likelihood methods

The effect of true Weibull modulus and sample size on Weibull modulus estimated by moments and maximum likelihood methods was investigated. Results indicated that the value of true Weibull modulus had no effect on estimated modulus for the maximum likelihood method, and a strong effect for the moments method, especially when sample size was less than 30. In addition, the distribution of Weibull modulus estimated by both methods was investigated using the modified Anderson–Darling statistics for goodness of fit. It was found that the distribution was not normal, lognormal, 3-parameter Weibull, or 3-parameter log-Weibull for the maximum likelihood method, as reported in previous studies. For the moments method however, the distribution of normalized Weibull moduli was found to be lognormal for sample sizes of 40 and above. The other three distributions showed a significant level of lack-of-fit at all sample sizes.