SURVIVAL ANALYSIS OF A NEW GENERALIZATION OF EXPONENTIALEXPONENTIAL DISTRIBUTION AND ITS APPLICATIONS TO CANCER DATA

ABSTRACT:In statistics literature there are so many distributions which need generalisation or extension tomake them more flexible and to aid their application in various fields like medicine, ecologyand reliability and so on. The generalisation and extension are done with the help of familiesof distributions. This article deals with a new generalization of exponential-exponentialdistribution named as exponentiated exponential-exponential distribution with scale and shapeparameters. Some statistical aspects of the novel distribution such as moments, momentgenerating and characteristic functions, mode and harmonic mean are derived. Reliability termssuch as survival function, hazard function and reverse hazard functions are discussed. The plotof the pdf, cdf and reliability functions also included. We derive Bonferroni and Lorenz curveand density of order statistics. Maximum likelihood method is employed for estimating theparameters of the distribution. The superiority (with the help of likelihood values, AIC, BIC,AICC and HQIC) of the new model with some existing distribution is illustrated through a twocancer data sets. The results showed that the new model is better fit.