Generalized Extreme Value Distribution using r-largest Order Statistics with Climate Application

This paper deals with usefulness of generalized extreme value distribution(r-GEVD) based on the r-largest order statistics. It is shown by simulation that using r-GEVD is better than using just the ordinary GEVD in estimating tail quantiles. Three parameters of GEVD are estimated by the method of maximum likelihood(MLE) and penalized maximum likelihood estimator(PMLE). This study compares the performance of two methods for several sample sizes and it is also shown that for small sample size, the mean square error of PMLE is magnificently improved than that of MLE with the concern of different extreme upper tail quantiles. The PMLE is employed with a suitably chosen beta penalty. The algorithm is developed for generating random numbers from r-GEVD. This approach is applied to extreme daily rainfall data for Seoul Korea. The return level of heavy rainfall is calculated from the r-GEVD model.