The Generalized Transmuted Lindley Inverse Exponential distribution properties and Applications to bladder cancer
DOI:
https://doi.org/10.33003/fjs-2026-1019-5396Keywords:
Generalized Transmuted Lindley-Inverse Exponential Distribution (GTLIED), Lifetime Data, Reliability Analysis, Survival Function, Hazard Function,, Maximum Likelihood EstimationAbstract
The Generalized Transmuted Lindley-Inverse Exponential Distribution (GTLIED) is introduced as a new flexible lifetime distribution developed by combining the generalized transmuted family of distributions with the Lindley-Inverse Exponential Distribution (LIED). The model is proposed to overcome the limitations of the classical exponential and inverse exponential distributions, particularly their inability to adequately model highly skewed lifetime data and varying hazard rate behaviors. The cumulative distribution function and probability density function of the GTLIED are derived, and its statistical properties, including moments, moment generating function, characteristic function, survival function, and hazard function, are obtained. Maximum likelihood estimation is employed for parameter estimation. The flexibility and practical usefulness of the proposed model are demonstrated through an application to remission times of 128 bladder cancer patients. The performance of the GTLIED is compared with several competing distributions, including the LIED, EIED, OLIED, OLomIED, IED, ExD, and Lindley distributions. Based on model selection criteria such as AIC, CAIC, BIC, HQIC, Anderson-Darling, Cramér–Von Mises, and Kolmogorov–Smirnov statistics, the GTLIED provides the best fit to the bladder cancer dataset. The findings indicate that the proposed distribution is highly flexible and effective for modeling positively skewed lifetime data encountered in reliability and survival studies
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