THE EG-LINDLEY DISTRIBUTION: A FLEXIBLE MODEL FOR NON-COMMUNICABLE AND CHRONIC DISEASE SURVIVAL ANALYSIS
The Luminescence and Scintillation Properties of Crystal and Ceramic
DOI:
https://doi.org/10.55766/sujst10093Keywords:
EG-Lindley Distribution, Survival Analysis, Hazard Function, Goodness-of-Fit, Biomedical Data Modelling, Maximum Likelihood MethodAbstract
This study introduces and evaluates the EG-Lindley (EG-L) distribution as a flexible model for analyzing survival data. The EG-L distribution is shown to capture a wide range of hazard rate behaviors - including increasing, decreasing, and bathtub-shaped patterns, making it highly adaptable to biomedical and reliability data analysis. A comprehensive analysis of the statistical properties of the EG-L distribution is presented, including the probability density function, cumulative distribution function, survival function, and hazard function, supported by detailed graphical interpretations. To assess the empirical performance of the EG-L distribution, three real-world datasets were analyzed: (1) bladder cancer patient survival times, (2) acute bone cancer survival data, and (3) head and neck cancer cases treated with radiotherapy and chemotherapy. The proposed model was compared with several existing generalizations of the Lindley distribution - namely, the New Generalized Two-Parameter Lindley Distribution, and the four other Generalized Lindley Distributions. Model performance was evaluated using goodness-of-fit criteria, including the -2log-likelihood, Akaike Information Criterion, Bayesian Information Criterion, Hannan–Quinn Information Criterion, and the Corrected Akaike Information Criterion. Across all datasets, the EG-L distribution consistently achieved the best or most competitive fit, as evidenced by the lowest information criteria values. These results underscore the robustness and adaptability of the EG-L distribution in capturing complex survival patterns and support its application as a valuable tool in the analysis of time-to-event data in clinical and epidemiological research.
References
Abouammoh, A. M., Alshangiti, A. M., & Ragab, I. E. (2015). A new generalized Lindley distribution. Journal of Statistical Computation and Simulation, 85(18), 3662-3678. https://doi.org/10.1080/00949655.2014.995101
Aderoju, S. (2021). Samade probability distribution: Its properties and application to real lifetime data. Asian Journal of Probability and Statistics, 14(1), 1-11.
Aderoju, S. A., & Babaniyi, O. (2023). Power Samade distribution: Its properties and application to real lifetime data. Nigerian Journal of Science and Environment, 21(1), 237-248.
Aderoju, S. A., Aleshinloye, N. I., Taiwo, B. L., & Sanni, B. I. (2023). A new lifetime distribution and its application to cancer data. Journal of Biostatistics and Epidemiology, 9(4), 451-460.
Aderoju, S., & Adeniyi, I. (2022). On power generalized Akash distribution with properties and applications. Journal of Statistical Modelling & Analytics, 4(1).
Ahsanullah, M., Ghitany, M. E., & Al-Mutairi, D. K. (2017). Characterization of the Lindley distribution by truncated moments. Communications in Statistics-Theory and Methods, 46(12), 6222-6227.
Aleshinloye, N. I., Aderoju, S. A., Abiodun, A. A., & Taiwo, B. L. (2023). A new generalized Gamma–Weibull distribution and its applications. Al-Bahir Journal for Engineering and Pure Sciences, 2(2), 90-100.
Edith, U. U., Ebele, T. U., & Henrietta, A. I. (2019). A two-parameter Rama distribution. Earthline Journal of Mathematical Sciences, 2(2), 365-382.
Ekhosuehi, N., Opone, F., & Odobaire, F. (2018). A new generalized two-parameter Lindley distribution. Journal of Data Science, 16(3), 549-566.
Everitt, B. S., & Hand, D. J. (1981). Mixtures of normal distributions. In Finite mixture distributions (pp. 25-57). Springer. https://doi.org/10.1007/978-94-009-5897-5_2
Ganaie, R. A., Rajagopalan, V., & Rather, A. A. (2020). On weighted two-parameter quasi-Shanker distribution with properties and its applications. International Journal of Statistics and Reliability Engineering, 7(1), 1-12.
Gemeay, A. M., Halim, Z., Abd El-Raouf, M. M., Hussam, E., Abdulrahman, A. T., Mashaqbah, N. K., Aljohani, H. M., & Makumi, N. (2023). General two-parameter distribution: Statistical properties, estimation, and application on COVID-19. PLOS ONE, 18(2), e0281474. https://doi.org/10.1371/journal.pone.0281474
Ghitany, M. E., Al-Mutairi, D. K., Balakrishnan, N., & Al-Enezi, L. J. (2013). Power Lindley distribution and associated inference. Computational Statistics & Data Analysis, 64, 20-33. https://doi.org/10.1016/j.csda.2013.02.026
Hamed, D., & Alzaghal, A. (2021). New class of Lindley distributions: Properties and applications. Journal of Statistical Distributions and Applications, 8, Article 8.
Irshad, M. R. (2017). New extended generalized Lindley distribution: Properties and applications. Statistica, 77(1), 33-52.
Lee, E. T., & Wang, J. W. (2003). Statistical methods for survival data analysis (3rd ed.). Wiley.
Lindley, D. V. (1958). Fiducial distributions and Bayes’ theorem. Journal of the Royal Statistical Society: Series B (Methodological), 20(1), 102-107. https://doi.org/10.1111/j.2517-6161.1958.tb00278.x
Makkar, P., Srivastava, P. K., Singh, R. S., & Upadhyay, S. K. (2014). Bayesian survival analysis of head and neck cancer data using lognormal model. Communications in Statistics-Theory and Methods, 43(2), 392-407. https://doi.org/10.1080/03610926.2012.664233
Mansour, M., Yousof, H. M., Shehata, W. A., & Ibrahim, M. (2020). A new two-parameter Burr XII distribution: Properties, copula, different estimation methods, and modelling acute bone cancer data. Journal of Nonlinear Science and Applications, 13(5), 223-238. https://doi.org/10.22436/jnsa.013.05.01
Miller, J. A. (2012). Species distribution models: Spatial autocorrelation and non-stationarity. Progress in Physical Geography, 36(5), 681-692. https://doi.org/10.1177/0309133312442522
Nadarajah, S., Bakouch, H. S., & Tahmasbi, R. (2011). A generalized Lindley distribution. Sankhya B, 73(2), 331-359.
Nadarajah, S., Cordeiro, G. M., & Ortega, E. M. (2015). The Zografos-Balakrishnan-G family of distributions: Mathematical properties and applications. Communications in Statistics-Theory and Methods, 44(1), 186-215.
Pararai, M., Oluyede, B. O., & Warahena-Liyanage, G. (2015). Kumaraswamy Lindley-Poisson distribution: Theory and applications. Asian Journal of Mathematics and Applications, 2015, ama0229.
R Core Team. (2025). R: A language and environment for statistical computing [Computer software]. R Foundation for Statistical Computing.
Shanker, R. (2020). A new quasi-Sujatha distribution. Statistics in Transition New Series, 21(3), 53-71. https://doi.org/10.21307/stattrans-2020-044
Shanker, R., & Mishra, A. (2013). A quasi-Lindley distribution. African Journal of Mathematics and Computer Science Research, 6(4), 64-71.
Wolstenholme, L. C. (2018). Reliability modelling: A statistical approach. Routledge. https://doi.org/10.1201/9780203740958
Zakerzadeh, H., & Dolati, A. (2009). Generalized Lindley distribution. Journal of Mathematical Extension, 3(2), 13-25.
