A New Generalization of the Gumbel Distribution With Climate Application
In this paper, we propose a new generalization of the Gumbel distribution named the Cubic Transmuted Gumbel distribution (CTGD) based on a cubic ranking transmutation map. Statistical properties of CTGD such as reliability function, hazard function, moments, moment generating function, quantile function, and simulation of the random sample are studied. The parameters of CTGD are estimated using the Maximum Likelihood method. Finally, an application of CTGD using two real data sets on climate change is conducted to illustrate and compare with the base Gumbel distribution (GD) and transmuted Gumbel distribution (TGD). CTGD was found to be a better fit than GD and TGD.