A New Logarithmic Family of Distributions: Properties and Applications

In recent years, there has been an increased interest among the researchers to propose new families of distributions to provide the best fit to lifetime data with monotonic (increasing, decreasing, constant) and non-monotonic (unimodal, modified unimodal, bathtub) hazard functions. We further carry this area of research and propose a new family of lifetime distributions called a new logarithmic family via the T-X family approach. For the proposed family, explicit expressions for some mathematical properties along with the estimation of parameters through Maximum likelihood method are discussed. A sub-model, called a new logarithmic Weibull distribution is taken up. The proposed model is very flexible and can be used to model data with increasing, decreasing, modified unimodal or bathtub shaped hazard rates. The maximum likelihood estimators of the model parameters are obtained. To assess the behavior of the maximum likelihood estimators, a comprehensive Monte Carlo simulation study has been carried out. Finally, the potentiality of the new model is shown via analyzing two real data sets taken from reliability engineering and biomedical fields. The comparison of the proposed model is made with the other well-known competitors such as (i) the three parameters exponentiated Weibull and Marshall-Olkin Weibull distributions and (ii) a four-parameter beta Weibull distribution. The practical applications show that the proposed model performs much better than the competitive models and can be used as a good candidate model to analyze data in engineering, medical sciences and other related fields.