On the q-Generalized Extreme Value Distribution
Keywords:extreme value theory, generalized extreme value distribution, goodness-of-fit statistics, Gumbel distribution, moments, Monte Carlo simulations, q-analogues
Asymmetrical models such as the Gumbel, logistic, Weibull and generalized extreme value distributions have been extensively utilized for modeling various random phenomena encountered for instance in the course of certain survival, financial or reliability studies. We hereby introduce q-analogues of the generalized extreme value and Gumbel distributions, the additional parameter q allowing for increased modeling flexibility. These extended models can yield several types of hazard rate functions, and their supports can be finite, infinite as well as bounded above or below. Closed form representations of some statistical functions of the proposed distributions are provided. It is also shown that they compare favorably to three related distributions in connection with the modeling of a certain hydrological data set. Finally, a simulation study confirms the suitability of the maximum likelihood method for estimating the model parameters.
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