The Mc-Donald Chen distribution: A new bimodal distribution with properties and applications

In this paper, the McDonald-Chen distribution is proposed and studied to model different type of data. Its probability density function allows bimodality, thus showing that the model is very flexible. Its failure or hazard rate function may have increasing, decreasing, bathtub, inverted bathtub and increasing-decreasing-increasing shapes depending on the parameter values. The new distribution includes at least five major special cases. Some of its mathematical properties are addressed. The maximum likelihood method is adopted to estimate the model parameters. Monte Carlo simulations evaluate the accuracy of the maximum likelihood estimators. The new distribution is better than three other popular distributions to model two real data sets.