This article introduces a bivariate Simplex distribution constructed via copula functions, particularly the Farlie–Gumbel–Morgenstern (FGM) copula, to model bounded continuous data defined on the unit interval. The proposed model allows flexible dependence structures while preserving analytical tractability. Maximum likelihood estimation procedures are derived, and extensive simulation studies are conducted to evaluate the performance of the estimators under different scenarios. Applications to real-world data, including mental health disorder prevalence and jurimetric indicators, illustrate the adequacy and interpretability of the proposed bivariate Simplex framework.
Alves et al. (Thu,) studied this question.