Also, the hazard rate function plots exhibit different shapes including decreasing, increasing, bathtub, J and reserved J shapes. It is observed that the density function plots of the distribution exhibit varying shapes and degrees of kurtosis. The density function and hazard rate function plots for different parameter values are obtained. Several properties of the distribution including the quantile function, moments, moment generating function, entropies and order statistics are derived. In this article, a new five parameter distribution, known as the modified beta flexible Weibull extension distribution, is derived and studied. The results show that the new distribution can serve as an alternative to modeling failure data sets. The distribution is used to model two real failure data sets to ascertain its usefulness. A bivariate extension of the distribution is also derived in the study. Various estimation methods are used to estimate the parameters of the distribution and a simulation study is conducted to ascertain the performance of the estimators. The numerical studies of the actuarial measures of the developed distribution are compared with other distributions. Also, several actuarial measures are derived. Several properties of the distribution including moments, moment generating function, inequality measures, order statistics and stochastic ordering are derived. The hazard rate function also shows shapes including decreasing, increasing, bathtub and modified bathtub shapes. The density function shows several shapes including skewed, approximately symmetric and decreasing shapes. The shapes of the density and hazard rate functions are obtained. The new distribution is a generalization of several well known distributions.
In this study, a new modified Weibull distribution, called the alpha power modified Weibull distribution, is proposed and studied.
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