MODIFICATION OF THE PROBABILITY MODEL USING THE ALPHA POWER TRANSFORMATION TECHNIQUE AND ITS EFFECT ON DIABETES SURVIVAL TIME DATA

ABSTRACT: Along with the changes in the patterns of data regarding the survival time of individuals with diabetes, often influenced by the consumption of unhealthy fast food. It is essential to update the appropriate probability model for this data. Twoparameter probability models, such as the Weibull, Gamma, and Log-Normal distributions, require modification by increasing the number of parameters in the probability model. The Alpha Power Transformation (APT) technique will be employed for this purpose. Three-parameter probability models generated from the APT technique, specifically, the Alpha Power Weibull Distribution (APWB), the Alpha Power Gamma Distribution (APGM), and the Alpha Power Log-Normal Distribution (APLN) will be employed to improve the accuracy of the probability model for diabetes survival time data. All probability models in this study will employ the maximum likelihood method for parameter estimation. The optimal model will be identified based on the goodness-of-fit test, which will incorporate both graphical methods (such as density graphs and cumulative distribution functions) and numerical methods (including the Akaike Information Criterion (AIC) and negative log-likelihood). The results of the goodness-of-fit tests indicate that the modified model obtained using the APT technique, particularly the APWB probability model, yields a superior probability model compared to the other models. KEYWORDS: Survival Time, Weibull, Gamma, Alpha Power Transformation, Alpha Power Weibull Distribution (APWB), the Alpha Power Gamma Distribution (APGM), and the Alpha Power Log-Normal Distribution (APLN).