Properties of new extension of Exponentiated exponential distribution with Application

Lifetime data modeling is vital topic that has received extensive attention in the modern statistical literature. This study aims to present a new distribution resulting from the expansion of the Exponentiated Exponential distribution using the [0,1] Truncated Nadarajah – Haghighi – G family, and this distribution is named [0,1]TNHEE several mathematical properties of the new distribution are studied, including density function, cumulative distribution, survival function, hazard function, moments, moment generated function, entropies (Shannon Rényi, and Delta), Lorenz and Bonforoni function, residual function, in addition to rank statistic and maximum likelihood estimators. The distribution was applied to real world data representing the survival times of 72 guinea pigs infected with tuberculosis. The results showed that the new distribution outperformed several competing distribution, including [0,10TEEEE, BeEE, KuEE, EGEE, and WeEE using statistical comparison criteria such as AIC, BIC, CAIC, and HQIC, as well as the Kolmogorov – Smirnov test, which yielded a high p-value (0.603), confirming the goodness of fit. The results showed that the new distribution has high flexibility and excellent interpretability for real-world data, making it a effective candidate for medical and engineering applications.