New Lifetime Distribution and its Application to Cancer Data

Abstract

Introduction: Recently, researchers have introduced new generated families of univariate lifetime distributions. These new generators are obtained by adding one or more extra shape parameters to the underlying distribution or compounding two distributions to get more flexibility in fitting data in different areas such as medical sciences, environmental sciences, and engineering. The addition of parameter(s) has been proven useful in exploring tail properties and for improving the goodness-of-fit of the family of the proposed distributions.
Methods: A new Three-Parameter Weibull-Generalized Gamma (for short, “TWGG”) distribution which provides more flexibility in modeling lifetime data is developed using a two-component mixture of Weibull distribution (with parameters  and Generalised Gamma distribution (with parameters . Some of its mathematical properties such as the density function, cumulative distribution function, survival function, hazard rate function, moment generating function, Renyi entropy and order statistics are obtained. The maximum likelihood estimation method was used in estimating the parameters of the proposed distribution and a simulation study is performed to examine the performance of the maximum likelihood estimators of the parameters.
Results: Real life applications of the proposed distribution to two cancer datasets are presented and its fit was compared with the fit attained by some existing lifetime distributions to show how the TWGG distribution works in practice. 
Conclusion: The results suggest that the proposed model performed better than its competitors and it’s a useful alternative to the existing models.