THE TRANSMUTED GOMPERTZ INVERSE RAYLEIGH DISTRIBUTION: PROPERTIES, ESTIMATION, AND APPLICATIONS

Abstract

This study introduces a new probability distribution, the Transmuted Gompertz Inverse Rayleigh (TGIR) distribution, developed by integrating the Gompertz Inverse Rayleigh distribution with the transmuted family of distributions. The probability density function of the TGIR model is unimodal and right-skewed, while its hazard rate function accommodates both increasing and bathtub-shaped patterns, making it suitable for modeling diverse lifetime data. Key analytical properties of the proposed model are derived, including expressions for the moments, moment generating function, Rényi entropy, mean residual life function, and order statistics. The parameters of the TGIR distribution are estimated using the method of maximum likelihood. A simulation study is conducted to evaluate the consistency and performance of the estimators. The practical utility of the TGIR model is demonstrated through its application to two real-life datasets, where it outperforms existing competing models based on various goodness-of-fit criteria.