The beta Nadarajah-Haghighi distribution

Recently, there has been a great interest among statisticians and applied researchers in constructing flexible distributions for better modeling non-monotone failure rates. We study a lifetime model of the beta generated family, called the beta Nadarajah-Haghighi distribution, which can be used to model survival data. The proposed model includes as special models some important distributions. The hazard rate function is an important quantity characterizing life phenomena. Its hazard function can be constant, decreasing, increasing, upside-down bathtub and bathtub-shaped depending on the parameters. We provide a comprehensive mathematical treatment of the new distribution and derive explicit expressions for some of its basic mathematical quantities. The method of maximum likelihood is used for estimating the model parameters and a small Monte Carlo simulation is conducted. We fit the proposed model to two real data sets to prove empirically its flexibility as compared to other lifetime distributions.