Umar, M. A.Jimoh, J.O.Garba, MohammedAfolayan, RazaqYahya, Waheed2021-10-122021-10-122019https://uilspace.unilorin.edu.ng/handle/20.500.12484/6594Exponential family of distribution is a very popular family of distribution functions for analyzing any lifetime data with a lot of applications in different fields of knowledge. This family has distribution functions whose survival, hazard and mean residual life functions are simple and easy to study. As a result, this family has been generalized, modified and mixed with other density functions to give more flexible density functions to facilitate better modeling and analysis. This study is carried out to apply some of these distributions to real life datasets from clinical sciences, remission times of a Bladder cancer dataset. The behaviours of these distributions were illustrated graphically. The parameters of the distributions were estimated using the maximum likelihood method and their goodness-of-fits were examined. The distributions were found to provide satisfactory fits to the datasets considered. Exponentiated Exponential and Exponential-Gamma distributions were found to perform better than all the competing distributions.enExponential familyGammaWeibullLindleyHazard rateMean residual lifeGoodness-of-fit.Other