A New Odd Reparameterized Exponential Transformed-X Family of Distributions with Applications to Public Health Data

In this study, we designed a new family of distributions called new odd reparameterized exponential transformed-X family of distributions. This was achieved by utilizing an exponential distribution with a constant scale parameter as the transformer and then the odd function of the baseline distribution as the generalizer. The new family was used to extend the classical Weibull distribution. We further studied the characteristics of the new extended Weibull distribution which include the quantile function, moment, moment generating function, mean residual life function, order statistic, entropy and extropy. Again, the parameters were estimated using both non-Bayesian and Bayesian approaches. A comprehensive Monte Carlo simulation was conducted under four different scenarios. The proposed distribution was fitted to HIV/AIDS and COVID-19 data and then compared with the baseline distribution (Weibull) and other related models. The new distribution commands superior fit with a probability value of 0.9959 and 0.7086 in the two datasets respectively.