DEVELOPMENT OF DOUBLE EXPONENTIAL-X FAMILY OF DISTRIBUTIONS

Abstract

The development of a new class of distributions has attracted the attention of both applied and theoretical statisticians in recent times due to flexibilities in their statistical properties. In this study, a new family of distributions named Double-Exponential-X family is proposed. The proposed family is generated from the double exponential distribution. Three unique subfamilies of the proposed family (Double-Exponential- Pareto, Double-Exponential Pareto II and Double-Exponential- BurrXII) are investigated and presented together with the shapes of their probability densities and hazard functions. General properties such as moment, survival, probability weighted moments and quartile functions of the models were investigated and established. Molecular simulation of efficacy of antiretroviral drugs was conducted to evaluate the performance of the model. Finally, real life data sets are used to illustrate the importance and application of the new family and their performance were compared to other well known competing models and also, stochastic dominance method was used to affirm the best antiretroviral drugs used in the study. The three subfamilies were tested and were found to be extremely skewed distributions. They were found to provide good fits to the molecular simulation of efficacy of antiretroviral drugs. The Double-Exponential Pareto distribution (DEPD) appears to give the best fit for the two drugs considered, Neviranpine and Abbacavir, with binding affinity of 45.12% and 52.09% respectively. The real life performance of the model was impressive when compared to well-known distributions. DEPD outperforms other two distributions (EPD and ED). It has a binding affinity of 65.6% as compared to 60.01% and 44.85% for EPD and PD respectively. And conclusions were made and some recommendations were also drawn for further studies