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In this paper, we propose a new flexible statistical distribution, the Topp-Leone Exponentiated Chen distribution, to model real-world data effectively, with a particular focus on COVID-19 data. The motivation behind this study is the need for a more flexible distribution that can capture various hazard rate shapes (e.g., increasing, decreasing, bathtub) and provide better fitting performance compared to existing models such as the Chen and exponentiated Chen distributions. The principal results include the derivation of key statistical properties such as the probability density function, cumulative distribution function, moments, hazard rate function, and order statistics. Maximum likelihood estimation is employed to estimate the parameters of the TLEC distribution, and simulation studies demonstrate the efficiency of the maximum likelihood method. The innovation of this work is further validated by applying the TLEC distribution to real COVID-19 data, where it outperforms several related models. The study concludes with significant insights into how the TLEC distribution provides a more accurate and flexible approach to modeling real-world phenomena.
