Abstract
In this article, a new five parameter distribution, known as the modified beta flexible Weibull extension distribution, is derived and studied. Several properties of the distribution including the quantile function, moments, moment generating function, entropies and order statistics are derived. The density function and hazard rate function plots for different parameter values are obtained. It is observed that the density function plots of the distribution exhibit varying shapes and degrees of kurtosis. Also, the hazard rate function plots exhibit different shapes including decreasing, increasing, bathtub, J and reserved J shapes. The parameter estimators of the distribution are obtained using maximum likelihood estimation. The estimators are found to be consistent via a simulation study. Finally, three data sets are used to assess the usefulness of the distribution. It is observed that the distribution can serve as an alternative to modelling failure time data with different characteristics.
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