The Weibull distribution is a two-parameter distribution that contains the exponential distribution as a special case and that is generalized to the extreme value type 3 distribution by a linear transformation. Its parameters and quantiles were estimated by the methods of moments, probability weighted moments, maximum likelihood estimation, entropy and least squares for Monte Carlo generated samples. The performance of these estimators was statistically compared, with the objective of identifying the most robust estimator from amongst them. Maximum likelihood and entropy demonstrated the most robustness compared to the other methods. Probability weighted moments performed well for samples which demonstrated large variability, while ordinary moments showed the least variability of estimates in the tails of the distribution from very small sample sizes.