Mixture Gumbel models for extreme series including infrequent phenomena

Abstract

A Gumbel mixture distribution is proposed for modelling extreme events from two different mechanisms: one phenomenon occurring annually and one occurring infrequently. A new Monte Carlo simulation procedure is presented and used to assess the consequence of fitting traditional Gumbel or GEV models to annual maximum series originating from two different populations. The results show that mixture models are preferred to single-population models when the two populations are very different. The Gumbel mixture model was applied to annual maximum 24-hour rainfall data from 64 South Korean raingauges, split into events generated by typhoon and non-typhoon rainfall. The results show that the use of a mixture model provides a more accurate description of the observed data than the Gumbel distribution, but is comparable to the GEV model. The theoretical and practical results highlight the need for more robust methods for identifying the underlying populations before mixture models can be recommended.