ADVANCED STATISTICAL APPROACH TO FAILURE DATA WITH GAMMA AND WEIBULL DISTRIBUTIONS

This paper aims to systematically investigate the utility of the Gamma and Weibull distributions, focusing on their application to biomedical datasets and clarifying their mathematical and statistical properties. By analyzing lifetime data across various disciplines, the research emphasizes the effectiveness and flexibility of these distributions in capturing the complexities of biomedical data. It underscores the importance of parameters such as standard error, log-likelihood, Akaike Information Criterion (AIC), and Bayesian Information Criterion (BIC) in value estimation. The findings suggest that both distributions provide valuable insights into the underlying data, with practical implications for reliability engineering and failure analysis. Moreover, the study demonstrates that the Weibull distribution offers a better fit to the given data than the Gamma distribution due to its adaptability, which yields superior results. A key contribution of this study is the proposal of a model based on estimating the Conditional Weibull distribution for feature parameters, which accurately predicts a finite mixture of two-parameter Weibull distributions initially verified on datasets.