Statistical Modelling of HIV/AIDS Mortality in the Kalyana Karnataka Region: A Comparative Analysis of Probability Distributions

Understanding mortality patterns is crucial for effective public health planning and resource allocation in the fight against HIV/AIDS.This study aims to identify the bestfitting probability distribution for modelling HIV/AIDS mortality in the Kalyana Karnataka region by comparing the Weibull, Gamma, and Log-Normal distributions.Using Maximum Likelihood Estimation (MLE) method, the parameters of these distributions were estimated, and model selection.The analysis utilised Log-Likelihood, Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Kolmogorov-Smirnov test, Cramer-von Mises test, and Anderson-Darling test as its foundational indicators.The findings indicate that the Weibull distribution provides the best fit, as it has the highest Log-Likelihood lowest AIC (843.8927) and BIC (848.8923), and the best goodness-of-fit statistics.The Gamma distribution was a close alternative, while the Log-Normal distribution exhibited the poorest fit.The superior performance of the Weibull model suggests that HIV/AIDS mortality follows a structured pattern, making it a valuable tool for mortality risk assessment and predictive modelling.These insights can aid policymakers in healthcare planning, intervention strategies, and resource allocation to mitigate HIV/AIDS-related deaths.