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 to
make them more flexible and to aid their application in various fields like medicine, ecology
and reliability and so on. The generalisation and extension are done with the help of families
of distributions. This article deals with a new generalization of exponential-exponential
distribution named as exponentiated exponential-exponential distribution with scale and shape
parameters. Some statistical aspects of the novel distribution such as moments, moment
generating and characteristic functions, mode and harmonic mean are derived. Reliability terms
such as survival function, hazard function and reverse hazard functions are discussed. The plot
of the pdf, cdf and reliability functions also included. We derive Bonferroni and Lorenz curve
and density of order statistics. Maximum likelihood method is employed for estimating the
parameters 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 two
cancer data sets. The results showed that the new model is better fit.