On The Burr III-Moment Exponential Distribution

Abstract

In this study, we introduce a new lifetime model derived from T-X family called Burr III moment exponential (BIII-ME) distribution. The shapes of the probability density and hazard rate functions for this model are obtained. The BIII-ME density function has bimodal, arc, symmetrical, left-skewed, right-skewed, J and reverse-J shapes. The proposed model can produce monotone and non-monotone failure rates shapes. To illustrate the importance of the proposed distribution, various mathematical properties of it are established such as ordinary moments, order statistics, conditional moments, reliability measures and Rényi entropy. The BIII-ME distribution is characterized via innovative techniques. The maximum likelihood estimates (MLE) for the model parameters are studied. The precision of the MLEs is estimated via a simulation study. We consider two applications to two real data sets to demonstrate the potentiality and utility of the BIII-ME model. Then, we establish empirically that the proposed model is suitable for strength of glass fibers and fracture toughness applications. Finally, the goodness of fit statistics and graphical tools are used to examine the adequacy of the BIII-ME distribution.