A Weibull-Gompertz Makeham Distribution with Properties and Application to Cancer Data
Peter O. Koleoso *
Department of Statistics, University of Ibadan, Ibadan, Nigeria.
Angela U. Chukwu
Department of Statistics, University of Ibadan, Ibadan, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
The article presents an extension of the Gompertz Makeham distribution using the Weibull-G family of continuous probability distributions proposed by Tahir et al. (2016a). This new extension generates a more flexible model called Weibull-Gompertz Makeham distribution. Some statistical properties of the distribution which include the moments, survival function, hazard function and distribution of order statistics were derived and discussed. The parameters were estimated by the method of maximum likelihood and the distribution was applied to a bladder cancer data. Weibull-Gompertz Makeham distribution performed best (AIC = -6.8677, CAIC = -6.3759, BIC = 7.3924) when compared with other existing distributions of the same family to model bladder cancer data.
Keywords: Gompertz-Makeham distribution, Weibull-Gompertz Makeham distribution, hazard function, survival function, cancer