Mixture Model of the Exponential, Gamma and Weibull Distributions to Analyse Heterogeneous Survival Data

Abstract

Aims: In this study a survival mixture model of three components is considered to analyse survival data of heterogeneous nature. The survival mixture model is of the Exponential, Gamma and Weibull distributions. Methodology: The proposed model was investigated and the Maximum Likelihood (ML) estimators of the parameters of the model were evaluated by the application of the Expectation Maximization Algorithm (EM). Graphs, log likelihood (LL) and the Akaike Information Criterion (AIC) were used to compare the proposed model with the pure classical parametric survival models corresponding to each component using real survival data. The model was compared with the survival mixture models corresponding to each component. Results: The graphs, LL and AIC values showed that the proposed model fits the real data better than the pure classical survival models corresponding to each component. Also the proposed model fits the real data better than the survival mixture models corresponding to each component. Conclusion: The proposed model showed that survival mixture models are flexible and maintain the features of the pure classical survival model and are better option for modelling heterogeneous survival data.