A New One-Parameter Distribution with Two Turning Points and Bathtub Shaped Failure Rate Function

Abstract

The frequent development of new lifetime distributions is borne of the desire to obtain adequate fits to complex data sets across various fields of study. A new one-parameter mixture distribution called Emrem distribution is proposed in this study. Mathematical properties of the distribution such as the moments and other related measures, the moment generating function, mean absolute deviations, entropy and reliability indices are discussed extensively. The pdf of the distribution can have two turning points while the hazard rate function has a bathtub shape. The maximum likelihood approach is used to estimate the parameter of the Emrem distribution. We have demonstrated the consistency property of the maximum likelihood estimate through simulations. Results obtained by comparing the fit of the Emrem distribution and fits of the competing distributions to a real data set indicate that the proposed model is capable of outperforming well-known and widely used continuous one-parameter distributions in several data analysis cases.