A new mixture of exponential and Weibull distributions: properties, estimation and relibilty modelling

In this study, we propose a novel two-parameter mixture distribution that combines the Exponential and Weibull distributions. We thoroughly analyze this new model and derive its statistical properties. To estimate the parameters of the model, we employ several well-established methods, including maximum likelihood, weighted least squares, Cramer-von-Mises, and Anderson Darling. To evaluate the performance of the new model, we conduct numerical experiments using real data sets. We compare the fit of our model with that of other competitive models commonly used in the field. The results clearly demonstrate that our proposed model outperforms the other models, providing a significantly better fit to the data. These findings highlight the potential of the new mixture distribution in accurately modeling and analyzing various types of data. The superior fit obtained with our model suggests its applicability in a wide range of fields, including reliability analysis, lifetime data modeling, and other areas where accurate distribution fitting is crucial for effective decision-making.