Authors:Gauss M. Cordeiro, Thiago G. Ramires, Edwin M. M. Ortega, and Rodrigo R. Pescim
We deﬁne the extended beta family of distributions to generalize the beta generator pioneered by Eugene et al. . This paper is cited in at least 970 scientiﬁc articles and extends more than ﬁfty well-known distributions. Any continuous distribution can be generalized by means of this family. The proposed family can present greater ﬂexibility to model skewed data. Some of its mathematical properties are investigated and maximum likelihood is adopted to estimate its parameters. Further, for different parameter settings and sample sizes, some simulations are conducted. The superiority of the proposed family is illustrated by means of two real data sets.
Authors:Morad Alizadeh, Mahdi Rasekhi, Haitham M. Yousof, Thiago G. Ramires, and G. G. Hamedani
In this article, a new four-parameter model is introduced which can be used in mod- eling survival data and fatigue life studies. Its failure rate function can be increasing, decreasing, upside down and bathtub-shaped depending on its parameters. We derive explicit expressions for some of its statistical and mathematical quantities. Some useful characterizations are presented. Maximum likelihood method is used to estimate the model parameters. The censored maximum likelihood estimation is presented in the general case of the multi-censored data. We demonstrate empirically the importance and exibility of the new model in modeling a real data set.