Innovative survival modeling in pandemics with a novel family of distributions: a comparative study of UK and Mexico pandemic data

Statistical approaches have broad applications in almost all areas of life, especially education, hydrology, reliability, administration, and healthcare. Statistical investigation and data forecasting are critical components of medical decision-making and outcome improvement. This article introduces an innovative generator based on the inverted trigonometric function, especially the Arccosecant Φ family of distributions, with the Burr distribution as the foundation model. This technique establishes the distributional features and adaptability of the Arccosecant-Burr distribution (for reference ACBD). The practicality of the model is demonstrated by comparing it to two datasets from the survival analysis. The first set of information indicates the fatality rate among individuals in Mexico who contracted coronavirus disease 2019 (COVID-19). The second data set shows the death rate of COVID-19 sufferers in the United Kingdom. Several estimation approaches are utilized to determine the unknown parameters of the ACBD distribution. The evaluation of these data sets reveals that the generator outperformed other models, indicating greater effectiveness.