In this work, we propose and study a novel generalization of the Fréchet distribution called the odd beta prime Fréchet (OBPF) distribution. This distribution was an extension of the Fréchet distribution by applying the odd beta prime generalized family of distributions. The proposed model can be expressed as a linear mixture of Fréchet densities. The shapes of the density function possess great flexibility. It can accommodate various hazard shapes, such as increasing, decreasing, and reversed J. Some important statistical properties of the OBPF are derived, including the ordinary and incomplete moments, order statistics, and quantile function. We have used the maximum likelihood estimation method to estimate the model parameters. The application and flexibility of the new distribution are empirically proven using groundwater pollution data sets compared to other competing distributions. The new model can be used instead of existing lifetime distributions and is suitable to fit data with right-skewed and left-skewed behaviors
Suleiman et al. (Tue,) studied this question.