A new exponentiated beta Burr type X distribution: model, theory, and applications - Oh, Yit Leng; Lim, Fong Peng; Chen, Chuei Yee; Ling, Wendy Shinyie; Loh, Yue Fang (Penerbit UKM, 2022)
In recent years, many attempts have been carried out to develop the Burr type X distribution, which is widely used in fitting lifetime data. These extended Burr type X distributions can model the hazard function in decreasing, increasing and bathtub shapes, except for unimodal. Hence, this paper aims to introduce a new continuous distribution, namely exponentiated beta Burr type X distribution, which provides greater flexibility in order to overcome the deficiency of the existing extended Burr type X distributions. We first present its density and cumulative function expressions. It is then followed by the mathematical properties of this new distribution, which include its limit behaviour, quantile function, moment, moment generating function, and order statistics. We use maximum likelihood approach to estimate the parameters and their performance is assessed via a simulation study with varying parameter values and sample sizes. Lastly, we use two real data sets to illustrate the performance and flexibility of the proposed distribution. The results show that the proposed distribution gives better fits in modelling lifetime data compared to its sub-models and some extended Burr type X distributions. Besides, it is very competitive and can be used as an alternative model to some nonnested models. In summary, the proposed distribution is very flexible and able to model various shaped hazard functions, including the increasing, decreasing, bathtub, and unimodal.