On the odd inverse exponential class of distributions: Properties, applications and cure fraction regression

In this paper, the generalized odd inverse exponential family of distributions is developed and studied. Statistical properties such as moments, moment generating function, incomplete moment, characteristic function and order statistics of the new family were derived. Two special distributions; generalized odd inverse exponential Weibull and generalized odd inverse exponential Lomax distributions were proposed. Again, regression models with cure fractions were developed using the special distributions. Four applications of the new family using cancer datasets suggest that the special distributions provide better fit to the datasets than the other fitted models.