The PWM large quantile estimates of heavy tailed distributions from samples deprived of their largest element / Estimation des grands quantiles de distributions à queue à décroissance lente par la méthode des moments pondérés par les probabilités à partir d'échantillons amputés de leur plus grande valeur

Abstract

Extremes of streamflow are usually modelled using heavy tailed distributions. While scrutinising annual flow maxima or the peaks over threshold, the largest elements in a sample are often suspected to be low quality data, outliers or values corresponding to much longer return periods than the observation period. In the case of floods, since the interest is focused mainly on the estimation of the right-hand tail of a distribution function, sensitivity of large quantiles to extreme elements of a series becomes the problem of special concern. This study investigated the sensitivity problem using the log-Gumbel distribution by generating samples of different sizes and different values of the coefficient of L-variation by means of Monte Carlo experiments. Parameters of the log-Gumbel distribution were estimated by the probability weighted moments (PWM) method, both for complete samples and the samples deprived of their largest element. In the latter case Hosking's concept of the “A” type PWM with Type II censoring was employed. The largest value was censored above the random threshold T corresponding to the non-exceedence probability F T. The effect of the F T value on the performance of the quantile estimates was then examined. Experimental results show that omission of the largest sample element need not result in a decrease in the accuracy of large quantile estimates obtained from the log-Gumbel model by the PWM method.