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The Topp-Leone distribution is widely used for modeling lifetime data across many disciplines. This paper presents the Exponentiated Cosine Topp-Leone Generalized family (ExCTLG), which is an extension of the Topp-Leone family. The research examines the mathematical properties of the ExCTLG, including the survival and hazard functions, moments, moment-generating functions, and Renyi’s entropy. Parameter estimation is carried out using the maximum likelihood estimation (MLE) techniques, and the estimated parameters consistency is validated using the Monte Carlo simulation method, thereby highlighting the superiority of MLE. The advantages and applicability of the proposed distribution are shown by analyzing two-lifetime datasets.
Osi et al. (Sat,) studied this question.