The transmuted GEV distribution: properties and application

The transmuted generalized extreme value (TGEV) distribution was first introduced by Aryal and Tsokos (Nonlinear Analysis: Theory, Methods & Applications, 71, 401–407, 2009) and applied by Nascimento et al. (Hacettepe Journal of Mathematics and Statistics, 45, 1847–1864, 2016). However, they did not give explicit expressions for all the moments, tail behaviour, quantiles, survival and risk functions and order statistics. The TGEV distribution is a more flexible model than the simple GEV distribution to model extreme or rare events because the right tail of the TGEV is heavier than the GEV. In addition the TGEV distribution can adjusted various forms of asymmetry. In this article, explicit expressions for these measures of the TGEV are obtained. The tail behavior and the survival and risk functions were determined for positive gamma, the moments for nonzero gamma and the moment generating function for zero gamma. The performance of the maximum likelihood estimators (MLEs) of the TGEV parameters were tested through a series of Monte Carlo simulation experiments. In addition, the model was used to fit three real data sets related to financial returns.