Cubic Transmuted Ailamujia Distribution - Type I: Statistical Properties and Application

This study introduces and evaluates the Cubic Transmuted Ailamujia Distribution (CTAD), a novel distribution developed using CRT-type I as a generator and the Ailamujia distribution as a baseline. We derived several statistical quantities, including density and distribution functions, hazard and survival functions, moments, and order statistics. The performance of the CTAD was compared against several established models using three distinct datasets: exceedances of flood peaks from the Wheaton River (Dataset I), cumulative COVID-19 death counts for Ghana (Dataset II), and daily confirmed COVID-19 cases for Ghana (Dataset III). The CTAD showed competitive performance, often outperforming traditional models such as the QTAD and Ailamujia distributions in Dataset I, and demonstrating strong performance relative to the CTGD, CTFD, and CTWD distributions in Dataset II. In Dataset III, while the CTAD was competitive, it was outperformed by the EWD and GGD in terms of AIC and BIC. Overall, the CTAD proves to be a robust and flexible distribution for modelling complex data patterns, though alternative distributions may offer better fits in specific scenarios. These findings underscore the CTAD’s potential as a valuable tool in statistical modelling and suggest opportunities for further research and refinement.