Extending a Level Three Order Polynomial Probability Model

Inverse and power extensions were derived for a three order polynomial probability distribution and studied in this paper as post-development. The two extensions serve to make up for the limitations of their baseline model. Some relevant properties—shape of the PDF, moments, survival function, hazard function, quantile function, stress-strength reliability, order statistics and parameter estimations—were studied. The hazard shapes of the distributions were found to be inverted bathtub for the former and three different shapes namely: increasing function, decreasing function and bathtub, for the latter. This implies that the distributions can altogether model many varieties of datasets emanating from different life phenomena. This statement “if S(∞)=0, then H(∞)=∞” was examined and was discovered to apply for exponential distribution but not any of the extended distributions, and the baseline distribution too. Finally, the extensions showed to be competent over both the baseline distribution and their respective counterpart distributions, with respect to the datasets used. For the latter, the superiority was accountably hinged on the extra parameters, since the dataset has an outlier.