Modeling Lifetime Data using the Hybridization Rama Distribution: Construction, Properties, Bayesian Estimation with Real-World Applications

Waleed M Afify (Department of Statistics, Mathematics and Insurance, Kafrelsheikh University, Kafrelsheikh-33511 (Egypt))
Eslam Abdelhakim Seyam (Department of Insurance and Risk Management, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh-13318 (Saudi Arabia))
Ahmed E Khairalla (Department of Statistics, Mathematics and Insurance, Kafrelsheikh University, Kafrelsheikh-33511 (Egypt))
Emadeldin I A Ali (Department of Mathematics, Statistics, and Insurance, Ain Shams University, Cairo-11566 (Egypt))
Said G Nassr (Department of Statistics and Insurance, Arish University, El-Arish-45511 (Egypt))
Ahmed Ramzy Shehata (Department of Statistics and Insurance, Arish University, El-Arish-45511 (Egypt))

Journal of Multidisciplinary Applied Natural Science
Vol. 6 No. 3 (2026): Journal of Multidisciplinary Applied Natural Science

This article introduces a novel hybrid probability distribution, termed the hybridization Rama (Hyb-R) distribution, constructed by integrating the proportional hazard model (PHM) within the rank transmutation map (RTM) framework, using the Rama distribution as a baseline. The proposed model aims to enhance flexibility and improve the modeling of lifetime data with skewness and kurtosis properties that standard distributions often fail to capture. We derive and explore the structural properties of the Hyb-R distribution, including its density and distribution functions, survival characteristics, and statistical measures. Parameter estimation is conducted using both classical methods via maximum likelihood estimation (MLE) and Bayesian methods under various loss functions (SEL, LINEX, and GEL), with implementation via the Metropolis-Hastings (MH) algorithm of Markov Chain Monte Carlo (MCMC) methods. A simulation study is performed to assess the accuracy and efficiency of the estimators. Results reveal that Bayesian estimators, particularly under informative priors and GEL, outperform MLEs in terms of lower mean square error and shorter credible intervals. The proposed Hyb-R model provides a flexible and effective alternative for modeling censored and real-world lifetime data.