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This paper introduces a novel compound distribution, named the Topp Leone Exponentiated Burr XII (TLEBXII) Distribution, aimed at generating a more flexible family of probability distributions. By taking the Exponentiated Burr XII distribution as the base and the Topp Leone exponentiated G family as the generator, this new distribution seeks to enhance modeling capabilities in various statistical applications. We present general expressions for the density and distribution functions of the TLEBXII model and explore its fundamental properties, including survival and hazard rate functions, moments, moment-generating functions, and entropy. Additionally, we discuss the methodology for estimating the model parameters through maximum likelihood estimation. The utility and superior performance of the TLEBXII distribution are demonstrated through its application to two real datasets, where it shows significant improvements over existing models. This paper underscores the potential of the TLEBXII distribution in providing a robust tool for statistical modeling and analysis.
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