Three identical mixture distributions approach to analyze composite survival data

Abstract

In this paper, a parametric mixture model of three identical (same) distributions of Exponential, Gamma, Log-normal, Weibull and Gompertz is considered to model composite or heterogeneous survival data. Mixtures of these three identical distributions were tested for the best fit by the simulated datasets as well as real time survival dataset. Some properties of the proposed parametric mixture of Exponential, Gamma, Weibull, Lognormal and Gompertz are investigated. The Expectation Maximization Algorithm (EM) is employed to estimate parameters of mixture models based on Maximum Likelihood method. Simulations are performed by generating data, sampled from a population of three component parametric mixtures of three identical distributions and the simulations have 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 to the postulated models, as the number of repetitions increases with relatively small standard errors. Akaike's information criterion (AIC) and goodness of fit tests are used for the comparison of model performances. Results revealed that the proposed model fits the real data better than the pure classical survival models corresponding to each component.