On robustness of large quantile estimates of log-Gumbel and log-logistic distributions to largest element of the observation series: Monte Carlo results vs. first order approximation.

Abstract

Robustness of large quantile estimates to the largest element in a sample of methods of moments (MOM) and L-moments (LMM) was evaluated and compared. Quantiles were estimated by log-logistic and log-Gumbel distributions. Both are lower bounded and two-parameter distributions, with the coefficient of variation (CV) serving as the shape parameter. In addition, the results of these two methods were compared with those of the maximum likelihood method (MLM). Since identification and elimination of the outliers in a single sample require the knowledge of the sample’s parent distribution which is unknown, one estimates it by using the parameter estimation method which is relatively robust to the largest element in the sample. In practice this means that the method should be robust to extreme elements (including outliers) in a sample.