Mixture Model of Different Distributions: A Simulation Study with Different Censoring and Mixing Probabilities

Yusuf Abbakar Mohammed, Suzilah Ismail

Abstract: Survival mixture model of three different distributions was proposed. The model consists of a mixture of Exponential, Gamma and Weibull distributions. Simulated data was employed to investigate the performance of the model by considering three different censoring percentages and two sets of mixing probabilities in ascending order and descending order. The simulated data were used to estimate the maximum likelihood estimators of the model by employing Expectation Maximization (EM). Hazard functions corresponding to the censoring percentages were investigated graphically. Parameters of the proposed model were estimated and were all close the values used in generating the data. Simulation was repeated 300 times and the mean square error (MSE) and root mean square error (RMSE) were estimated to assess the consistency and stability of the model. The simulated data used to compare the effect of different censoring percentages revealed that the model performed much better with small percentage of censored observations. Also the model performed well with both the ascending and descending order of the mixing probabilities. However, mixing probabilities in ascending order performed better than the descending order. The hazard function graphs showed that, samples with higher percentage of censored observations seemed to have lower hazard compared to the smaller censored observations. 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.

Keywords: exponential, gamma, mixing probability, mixture model, Weibull