Comparative Evaluation of Gamma, Exponentiated Gamma, Weibull, and Exponentiated Weibull Distributions for Modeling Cervical Cancer Data
Résumé
This study evaluated the performance of four continuous probability distributions—Gamma, Exponentiated Gamma, Weibull, and Exponentiated Weibull—for modeling cervical cancer data. The parameters of each model were estimated using the maximum-likelihood method, and model adequacy was assessed through the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Log-Likelihood (LL), and diagnostic plots. The Gamma distribution produced shape and rate parameters of 0.7082 and 0.2669 with AIC = 641.07, BIC = 647.28, and LL = –318.53. The Exponentiated Gamma distribution yielded AIC = 174.97, BIC = 181.18, and LL = –318.53. The Weibull distribution gave shape = 0.8377 and rate = 0.5778 with AIC = 174.57, BIC = 180.79, and LL = –85.29, while the Exponentiated Weibull recorded AIC = 278.93, BIC = 288.25, and LL = –136.47. Comparative analysis showed that the Weibull model achieved the lowest AIC and BIC and the highest Log-Likelihood, indicating the best overall performance. Diagnostic plots confirmed that the Weibull curve aligned most closely with the observed data, with minimal deviations on the cumulative and P–P axes. These findings demonstrate that the Weibull distribution provides the most parsimonious and statistically sound model for representing cervical-cancer data, consistent with previous reports on cancer survival modeling. The results support the use of the Weibull model as a baseline for predictive and risk-assessment applications in oncology research.
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