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Abstract
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Recently, there has been a great interest among statisticians and applied researchers in constructing exible 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, upsidedown 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 t the proposed model to two real data sets to prove empirically
its exibility as compared to other lifetime distributions.
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