SOME CONTRIBUTIONS TO ODD FAMILY OF DISTRIBUTIONS WITH APPLICATIONS TO CANCER DATASETS

Abstract

A new family of distributions, by name generalized odd inverse exponential distribution was developed in this study. The new family of distributions were developed using the concepts of relative odds. The statistical properties such as quantile function, characteristic function, moments, moment generating function, mean residual life, inequality measures and order statistics for the new family of distributions were obtained. The maximum likelihood, ordinary least squares and Cramér-von Mises procedures were employed to develop the estimators for the parameters of the new family of distributions. The study also derive some special distributions from the generalized odd inverse exponential family of distributions and these are; Generalized odd inverse exponential Weibull and generalized odd inverse exponential Lomax distributions. The hazard rates of these special distributions indicates that they can handle datasets that exhibit different kinds of non-monotonic failure rates. Again, regression models with cure fraction were developed using the special distributions. Monte Carlo simulations were performed to examine the behavior of the estimators and the results indicates that the estimators were consistent and that the maximum likelihood estimator was the best. The applications of the special distributions were demonstrated using eight cancer datasets and their performances were compared to other well-known existing distributions. The results showed that the special distributions perform better than the other existing distributions in terms of modeling cancer datasets.