A Study of the Mixture of Loglogistic-Loglogistic, LoglogisticGamma Distributions for the Analysis of Heterogenous Survival Data

Othman Musa Yakubu1, Yusuf Abbakar Mohammed1 and Akeyede Imam2

1Department of Mathematical Sciences, University of Maiduguri
2Department of Mathematics, Federal University Lafia, Lafia

*Corresponding author: othmanyakub@gmail.com, doi.org/10.55639/607. 171615


Failure time data are used in survival analysis. The traditional parametric and nonparametric methods of survival analysis must be modified since the existence of censoring renders them inadequate. When one classical model may not be enough, parametric mixture models are used. To handle the heterogeneity of survival data, a more robust parametric mixture is required. For the study of survival data, this paper proposed a mixture of two distributions; the models are the Loglogistic-Loglogistic and Loglogistic-Gamma distributions. The models’ performance was investigated using simulated data, and several iterations were run to test consistency. Expectation Maximization (EM) was employed to calculate the models’ maximum likelihood parameters. The computed model parameters all fell within a narrow range of the postulated values. The models’ consistency and stability were tested repeatedly through simulations using mean square error (MSE) and root mean square error (RMSE), and all were found to be stable and consistent. Real data were used to compare the fit of mixture models and classical distributions using information criteria (AIC). The best fit for the data was found using mixture models, which combine two different distributions. i.e., Loglogistic-Gamma distribution.


Survival analysis,