A mixture of weibull hazard rate with a power variance function frailty

A traditional approach in the analysis of survival data was assumed a homogeneous population, i.e., all individuals had the same risk of failure or death. For this purpose, the Weibull distribution was very popular, especially in survival analysis. However, most populations consisted of individuals that differed in their susceptibility to causes of death or disease, responses to treatments and influences of various risk factors. This heterogeneity of responses when faced with unexplained factors could cause serious problems when dealt with by traditional methods since it could lead to misleading conclusions. This paper proposed a mixture of two distributions; Weibull hazard rate with a power variance function frailty distribution to model hazard rate. The proposed model included a mixture Weibull hazard rate with gamma and inverse Gaussian distribution. In additional, the parameter estimation for this model via maximum likelihood method was provided. The paper demonstrated its usefulness by applying it to a real data set. The results obtained indicated that the proposed model provided a better fit than the standard Weibull distribution.