A new lifetime model with decreasing, increasing, bathtub-shaped, and upside-down bathtub-shaped hazard rate function

A new three-parameter distribution with decreasing, increasing, bathtub-shaped and upside-down bathtub-shaped hazard rate function is proposed. The new distribution encompasses some previously known distributions as special cases. Basic mathematical properties of the new distribution (including the moment-generating function, moments, order statistics properties, Renyi entropy and stress–strength parameter) are derived. Its parameters are estimated by the method of maximum likelihood. An application is illustrated using a real data set.