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This paper proposes a new life distribution with both unbounded and bounded support. The proposed Extended Exponentiated Lomax (EEtLx) distribution is derived from the New Extended Exponentiated-G (NEET-G) family of Elgarhy, Haq, Gozel, and Nasir (2017). The maximum likelihood estimation method is used to estimate parameters of the proposed distribution and derive the relevant properties. The model is applied to patient relief times (minutes) after receiving a particular analgesic using different selection criteria (Log likelihood, Akaike Information Criteria (AIC), and Bayesian Information Criteria (BIC)). Resulting distributions are compared to well-established lifetime distributions in literature. The total time on test (TTT) plot is also used to determine whether the hazard rate function for this data increases or decreases, which subsequently reveals a decreasing trend. The proposed distribution remains the best fit compared to competing distributions. It is recommended that this distribution can be applied, not only in medical science, but also in reliability science, engineering, and economics fields.
Odunayo et al. (2024) studied this question.