Cubic Rank Transmuted Akash Distribution: Model, Properties, and Applications in Cancer Research

ABSTRACT Over the years, hundreds of new statistical distributions have been developed, and the demand for new distributions is rising. In engineering and biomedical applications, lifespan data modeling has extensively utilized the Akash distribution. However, significant skewness, large tails, and non‐monotone hazard patterns, which are frequently seen in survival data, are difficult for it to depict due to its single‐shape construction. To overcome this limitation, this paper proposes the cubic rank transmuted Akash (CRTA) distribution, which modifies the Akash distribution using the cubic rank transmutation technique to create a new, adaptable statistical model for examining survival and death rates associated with different types of cancer. The proposed modification introduces two additional shape parameters, significantly enhancing the flexibility of the baseline Akash model. To guarantee the validity of the CRTA distribution, a corrected admissible parameter space is created. The probability density function, distribution function, hazard rate, and moments are among the essential mathematical characteristics of the CRTA distribution that are derived. Additionally, moments, order statistics, stochastic ordering, moment generating function, mode, and median of the new distribution are also discussed. Maximum likelihood estimation is used to estimate model parameters. To ensure the reliability of the parameter estimation method, a simulation study was implemented to assess its consistency. Using actual cancer remission‐time statistics, the CRTA distribution's performance is assessed and contrasted with that of the Akash distribution and other popular competing models. The suggested distribution offers a better fit to the cancer data sets, as indicated by log‐likelihood, AIC, BIC, and Kolmogorov–Smirnov statistics. These findings demonstrate that the cubic rank transmutation method yields substantial improvements in survival modeling. The proposed model provides a solid foundation for future extensions utilizing Bayesian and machine learning‐based estimation techniques, as well as a dependable statistical tool for biomedical survival analysis and engineering reliability.