The probability models of two and three mixed gamma distributions, specifically the Lindley and Sujatha distributions, will be enhanced through the application of random variable transformation techniques, resulting in the Power Lindley and Power Sujatha probability models. This study employs four probability models: Lindley, Sujatha, Power Lindley, and Power Sujatha, to analyze the survival time of diabetic patients. All probability models in this study will utilize the maximum likelihood method for parameter estimation. The optimal model will be determined based on a goodness-of-fit test, which will incorporate both graphical methods (density and cumulative distribution graphs) and numerical methods (Akaike's Information Criterion (AIC) and negative log-likelihood). The results of the goodness-of-fit test indicate that the model derived from the random variable transformation yields a superior probability model compared to its original form.