The transmuted XLindley distribution: Properties and estimation with biomedical survival applications

The development of flexible probability distributions are essential for accurately modeling lifetime data in radiation-exposed systems and biological entities. This study introduces the transmuted XLindley distribution, a novel probability distribution derived using the quadratic rank transmutation map applied to the XLindley distribution. The proposed distribution accommodates various hazard rate structures such as increasing trends, decreasing trends, and bathtub-shaped patterns often observed in radiation effects and reliability data. Several properties of the proposed distribution are explored, including explicit expressions for its moments, reliability function, stochastic comparison and order statistics. To estimate the model parameters we employ several classical and robust estimation techniques such as the maximum likelihood method, ordinary and weighted least squares, Anderson-Darling and Cramer-von Mises methods. In addition, approximate confidence intervals are obtained. The practical utility of the proposed model is demonstrated through real-life biomedical datasets that include cancer survival times. These applications highlight the model's strong performance in capturing data characteristics and predicting reliability measures. By effectively modeling skewed distributions with heavy tails and complex hazard rate patterns, the transmuted XLindley distribution shows strong potential for use in radiation research, medical physics, survival analysis and reliability studies in engineering systems. • Proposes a novel transmuted XLindley distribution using quadratic rank transmutation. • Effectively models complex hazard patterns in survival and radiation data. • Offers analytical expressions for moments, reliability function, and order statistics. • Evaluates parameter estimation via classical and robust statistical techniques. • Demonstrates superior fit on biomedical datasets including cancer survival times. • Applicable to engineering systems in reliability and radiation risk assessment.