On alternative q-Weibull and q-extreme value distributions: Properties and applications

Tsallis statistics and Tsallis distributions have been attracting a significant amount of research work in recent years. Importantly, the Tsallis statistics, q-distributions have been applied in different disciplines. Yet, a relationship between some existing q-Weibull distributions and q-extreme value distributions that is parallel to the well-established relationship between the conventional Weibull and extreme value distributions through a logarithmic transformation has not be established. In this paper, we proposed an alternative q-Weibull distribution that leads to a q-extreme value distribution via the q-logarithm transformation. Some important properties of the proposed q-Weibull and q-extreme value distributions are studied. Maximum likelihood and least squares estimation methods are used to estimate the parameters of q-Weibull distribution and their performances are investigated through a Monte Carlo simulation study. The methodologies and the usefulness of the proposed distributions are illustrated by fitting the 2014 traffic fatalities data from The National Highway Traffic Safety Administration.