On the new modified Dagum distribution: Properties and applications

In this paper, a new five parameter extended Dagum model called new modified Dagum (NMD) distribution is proposed. The proposed distribution is flexible as its density contains important sub-models such as modified Dagum, new Dagum, new modified Burr III, modified Burr III, Frechet, modified Frechet and many other distributions. The NMD density function is symmetrical, left-skewed, right-skewed, J, reverse-J and arc. The NMD distribution can produce all types of failure rates such as modified bathtub, bathtub, inverted bathtub, increasing and decreasing. To show the importance of the proposed distribution, we derive mathematical properties such as random number generator, sub-models, ordinary moments, moment generating function, characteristic function, incomplete moments, inequality measures, residual life functions and reliability measures. We characterize the NMD distribution via innovative techniques. We address the maximum likelihood estimation technique for the model parameters. We evaluate the precision of the maximum likelihood estimators via simulation study on the basis of the graphical results. We consider an application to a real data set to clarify the potentiality and utility of the NMD model. We establish empirically that the proposed model is suitable for survival times of patient's application. We apply goodness of fit statistics and graphical tools to examine the adequacy of the NMD distribution.