Statistical Modelling of Bladder Cancer Remission Data of Fluctuating Hazard Rate: An Inverse Power Pranav Distribution Approach

This study introduces the Inverse Pranav Distribution (IPD) as a flexible model for survival data with both monotone and non-monotone hazard rate behaviors. The Pranav distribution was inversely transformed to create the model, and its main statistical characteristics were determined. Using data on bladder cancer patients' remission times, the IPD's performance was contrasted with that of the Inverse Rama, Inverse Lindley, Inverse Exponential, and Inverse XGamma distributions. Based on likelihood values, information criteria, and goodness-of-fit tests, the results indicated that the IPD offered the best overall fit, outperforming rival models. The distribution was appropriate for survival and reliability studies because it could capture intricate hazard structures, including decreasing, increasing, and bathtub-shaped patterns.