A New Bivariate Family of Distributions Based on the Clayton Archimedean Copula and Dagum Distribution

This study introduces a novel bivariate distribution combining the Clayton Archimedean copula and the Dagum distribution, addressing challenges in modeling complex dependencies, skewness, heavy tails, and multimodal distributions. The proposed NBCDagE distribution leverages the Clayton copula’s ability to capture asymmetric dependencies and the Dagum distribution’s flexibility to model diverse data behaviors, making it suitable for reliability, finance, and survival analysis applications. Key statistical properties of the NBCDagE distribution, including the probability density function (PDF), cumulative distribution function (CDF), product and joint moments, and Shannon entropy, were derived and analyzed. The model demonstrates sensitivity to parameter changes, with higher parameter values leading to sharper PDFs and lighter tails, while lower values result in flatter PDFs and heavier tails. Joint moments and entropy analyses revealed the distribution’s ability to adapt to varying data complexities, showcasing its robustness in capturing dependence structures and marginal characteristics. Visual representations, including contour plots and density curves, illustrate the flexibility of the NBCDagE model in handling a wide range of dependence patterns and data structures. The distribution’s performance was further validated through theoretical derivations and numerical examples, highlighting its adaptability and precision in multivariate data modeling. In conclusion, the NBCDagE distribution provides a robust framework for analyzing bivariate data with intricate dependency structures. Its flexibility and statistical rigor make it a valuable tool for diverse applications, paving the way for future research in higher-dimensional extensions and practical implementations.