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In this paper, we consider different estimators of the quantiles of two-parameter Gumbel distribution. We use methodologies known as maximum likelihood, modified maximum likelihood and probability weighted moment to obtain the estimators of the quantiles. We compare the performances of the estimators with respect to bias and mean square error criteria via Monte Carlo simulation study. Their robustness properties are also examined in the presence of data anomalies. In the real data analysis part of the study, the seasonal maximum daily wind speed data from Sinop station (Turkey) in 2015 is considered. It is modelled by using two-parameter Gumbel distribution and analysed to compare the performances of the methodology presented in the study. All in all, the results of simulations and the real data application show that the maximum likelihood and modified maximum likelihood estimators, which have similar performance, provide better performance than the probability weighted moment estimator does in both obtaining estimates of the quantiles of Gumbel distribution and modelling of the data for almost all cases.

ESTIMATION OF THE LOWER AND UPPER QUANTILES OF GUMBEL DISTRIBUTION: AN APPLICATION TO WIND SPEED DATA