A new extended Pham distribution for modelling cancer data

In this study, a novel extended Pham model is offered and examined. This model can fit positive, negative, and approximately symmetric data. In addition, it features four alternative hazard rate shapes, namely increasing, decreasing, bathtub, and upside-down bathtub shapes. The new model's main properties, such as quantiles, moments, and mean deviations, are derived. To evaluate the estimation of distribution parameters, two approaches are studied. From a classical standpoint, the maximum likelihood technique is used to determine the point and approximate confidence intervals of all unknown parameters. The Bayesian estimation method, on the other hand, is considered via the Markov chain Monte Carlo technique for obtaining Bayes point estimates alongside Bayes credible intervals. We present various Monte Carlo simulation studies to investigate the efficacy of maximum likelihood and Bayes estimation findings for the model's parameters. Numerical investigations showed that the offered Bayes estimates outperformed those derived using the conventional method. We also analyzed two sets of real data taken from the medical sector; the first represents survival rates for cancer patients who received a combination of radiotherapy and chemotherapy, and the second consists of remission times for bladder cancer patients. These clinical scenarios reveal that the new model outperforms other important competing models based on specific statistical criteria. Ultimately, for both clinical data applications, the proposed extended Pham distribution is the best choice compared to the traditional Pham and the other well-known eight lifetime models.