Exponentiated gamma Burr-type X distribution: model, theory, and applications

Several extended Burr-type X distributions have been formed in the past decade. These distributions are widely used in modeling lifetime data as their hazard functions can fit various shapes, such as bathtub, decreasing, and increasing. However, certain extended Burr-type X distributions may not adequately fit the unimodal hazard function. Thus, this paper proposes a new extended distribution with greater flexibility to solve this deficiency: exponentiated gamma Burr-type X distribution. We provide the expressions for the probability density and cumulative distribution functions of the proposed distribution, along with its statistical properties, such as limit behavior, quantile function, moment function, moment-generating function, Renyi entropy, and order statistics. To estimate the model parameters, we employ the maximum likelihood estimation method, and we assess its performance through a simulation study with different sample sizes and parameter values. Finally, to demonstrate the application of this new distribution, we apply it to a real dataset concerning the failure times of aircraft windshields. The results indicate that the new distribution provides a superior fit compared to its submodels and the extended Burr-type X distributions. Moreover, it proves to be highly competitive and can serve as an alternative to certain nonnested models. In summary, the new distribution is highly flexible, capable of modeling a variety of hazard-function shapes, including decreasing, increasing, bathtub, and unimodal patterns.