The Gumbel model is a very popular statistical model due to its wide applicability for instance in the course of certain survival, environmental, financial or reliability studies. In this work, we have introduced a bimodal generalization of the Gumbel distribution that can be an alternative to model bimodal data. We derive the analytical shapes of the corresponding probability density function and the hazard rate function and provide graphical illustrations. Furthermore, We have discussed the properties of this density such as mode, bimodality, moment generating function and moments. Our results were verified using the Markov chain Monte Carlo simulation method. The maximum likelihood method is used for parameters estimation. Finally, we also carry out an application to real data that demonstrates the usefulness of the proposed distribution.
翻译:Gumbel模型是一个非常流行的统计模型,因为它具有广泛应用性,例如在某种生存、环境、财务或可靠性研究过程中。在这项工作中,我们采用了对Gumbel分布的双式统称,可以替代模型双式数据。我们从相应的概率密度函数和危险率函数中得出分析形状,并提供图形图解。此外,我们讨论了这种密度的特性,例如模式、双式、瞬时生成功能和瞬间。我们的结果用Markov链 Monte Carlo模拟方法进行了核实。最大可能性方法用于参数估计。最后,我们还对真实数据进行了应用,以显示拟议的分布的有用性。