摘要：Asymmetrical models such as the Gumbel, logistic, Weibull and generalized extremevalue distributions have been extensively utilized for modeling various random phe-nomena encountered for instance in the course of certain survival, financial or relia-bility studies. We hereby introduce q-analogues of the generalized extreme value andGumbel distributions, the additional parameter q allowing for increased modeling flex-ibility. These extended models can yield several types of hazard rate functions, andtheir supports can be finite, infinite as well as bounded above or below. Closed formrepresentations of some statistical functions of the proposed distributions are provided.It is also shown that they compare favorably to three related distributions in connec-tion with the modeling of a certain hydrological data set. Finally, a simulation studyconfirms the suitability of the maximum likelihood method for estimating the modelparameters.
关键词：extreme value theory; generalized extreme value distribution; goodness-of-fit statistics;Gumbel distribution; moments; Monte Carlo simulations; q-analogues.
