Abstract
Effective analysis of medical data is essential for understanding complex healthcare phenomena. Probability distribution models offer a structured approach to uncover patterns in such data, particularly for studying disease progression, survival analysis and many more. In this study, we explore a novel probability distribution model, derived by applying the DUS transformation to the standard Rayleigh distribution. We thoroughly investigate the statistical properties of the proposed model and derive key reliability measures to demonstrate its applicability in reliability analysis. To ensure precise parameter estimation, various estimation methods are evaluated, and their effectiveness is assessed through a detailed simulation study using bias, mean squared error, and mean relative error as performance criteria. The developed model's practical applicability is demonstrated with an analysis of COVID-19 data, comparing its performance with several well-known distributions. The results highlight the flexibility and accuracy of the model, establishing it as a powerful and reliable tool for advanced statistical modelling in healthcare research.