Heterogeneous Survival time data can have two different distributions before and after a certain time due to many factors which affects the life of the creatures or machines. For this purpose, we examine a mixture of two non-identical (different) distributions of Exponential, Gamma, Log-normal, Weibull and Gompertz distributions. In addition to the previous studies, we propose the mixture of Gompertz distribution with the Exponential, Gamma, Weibull and Lognormal distributions. Some properties of the proposed parametric mixture of Exponential, Gamma, Weibull, Lognormal and Gompertzare investigated. Both simulated and real data set were used to estimate the maximum likelihood estimators of the model by employing the Expectation Maximization (EM) algorithm method. The simulations are performed by generating data, sampled from a population of two component parametric mixture of two different distributions. The parameters estimated by the proposed EM Algorithm which are closer to the parameters of the postulated model. To investigate the consistency and stability of the EM algorithm, the simulations are repeated several times. The repetitions of the simulation give estimators closer to the values of postulated models, with relatively small standard errors. Graphs, goodness of fit tests 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. Results revealed that the proposed model showed that a parametric mixture models are more flexible and maintainthe features of the pure classical survival model and are better option for modelling heterogeneous survival data.
