A novel bivariate regression model derived from the clayton copula and the Odd Dagum-G family and its application

This study presents a new bivariate regression model that is generated from the Clayton Copula and the Odd Dagum-G (OddD-G) family. Many of the current bivariate regression models including those based on the bivariate normal and t-distributions assume symmetric dependencies, therefore restricting their relevance to real-world data where dependence structures are commonly asymmetric or bimodal. This limitation poses a challenge in fields like biostatistics, finance, agriculture and hydrology where complex dependencies is crucial for reliable inference. The new model adopts a more flexible framework to model the dependencies enhancing precision in multivariate analysis. The models cumulative distribution function (CDF) and probability distribution function (PDF) are derived and the parameters were estimated using the maximum likelihood estimation (MLE) where the likelihood function was optimized using the Broyden-Fletcher-Goldfarb-Shannon (BFGS) algorithm. Simulation is conducted under various scenarios to validate the model’s robustness, exhibiting consistent estimators, reduced bias, and decreasing mean square errors (MSEs) with increasing sample size. The reliability of the estimators is also supported by the empirical coverage probabilities generated. The model is applied to an experimental dataset on kale plants to explore the relationship between its fresh weight and plant height under different treatments. Univariate models are first applied to the data and was assessed using Akaike Information Criterion (AIC) and Global Deviance (GD) which also proved effective in the bivariate cases among existing models. These results highlight its flexibility and potential to improve statistical analysis, especially for complex dependencies in real-world data.