The transmuted cosine–shanker distribution: Properties and applications in reliability analysis

Abstract

The Transmuted Cosine–Shanker (TC-Shanker) model, a novel and adaptable probability distribution, is presented in this study. It is created by combining the cosine-G and transmuted-G families. The Cosine–Shanker model is generalized by the TC-Shanker distribution by adding a second shape parameter, λ, where |λ| ≤ 1, to provide more modeling flexibility for complex and skewed real-world data. The probability density function, cumulative distribution function, survival function, hazard rate function, moments, moment generating function, and quantile function are among the basic statistical characteristics that we derive. A comprehensive simulation study demonstrates the consistency and efficiency of the maximum likelihood estimators for the distribution parameters. The practical utility of the TC-Shanker model is validated using both complete and censored real-world datasets: one on milk production from cattle, another on pediatric leukemia remission times, and a third on lung cancer survival.

In all cases, applications, the TC-Shanker distribution offers better fit as compared with several competing models, as indicated by lower levels of the information criteria statistics (AIC, CAIC, BIC) and better goodness-of-fit statistics. The results verify further that TC-Shanker distribution is a robust and versatile tool for lifetime data analysis in fields such as biostatistics, reliability engineering and medical research.