Mixture of identical distributions of exponential, gamma, lognormal, weibull, gompertz approach to heterogeneous survival data

In this paper, a parametric mixture model of two identical distributions is proposed to analyze heterogeneous survival data. Mixtures of Exponential-Exponential, Weibull-Weibull, Gamma-Gamma, Lognormal-Lognormal and Gompertz-Gompertz distributions were tested for the best fit to the simulated datasets as well as real survival datasets. Various properties of the proposed mixture models were discussed. The Expectation Maximization Algorithm (EM) is implemented to estimate the maximum likelihood estimators of the parameters of mixture models. Simulations were performed by simulating data, each randomly sampled from a population of two component parametric mixture model of identical distributions and the simulations has been repeated 500, 1000, 5000 times with samples of size 100 observations for each mixture model to investigate the consistency and stability of the EM algorithm. The repetitions of the simulation give estimators closer and closer to the postulated models, as the number of repetitions increases with relatively small standard errors. Model performances are compared using goodness of fit tests and Akaike's information criterion(AIC). Results revealed that the proposed model fits the real data better than the pure classical survival models corresponding to each component.