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Bivariate Simplex Distribution
Distribución Simplex Bivariada
DOI:
https://doi.org/10.15446/rce.v49n1.118380Keywords:
Bivariate Simplex distribution, Copulas, FGM copula, Maximum likelihood estimation (en)Distribución Simplex bivariada, Cópulas, Cópula FGM, Estimación por máxima verosimilitud, Datos acotados (es)
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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.
Este artículo introduce una distribución Simplex bivariada construida mediante funciones cópula, en particular la cópula de Farlie–Gumbel–Morgenstern (FGM), para modelar datos continuos acotados en el intervalo unitario. El modelo propuesto permite estructuras de dependencia flexibles conservando la tractabilidad analítica. Se desarrollan procedimientos de estimación por máxima verosimilitud y se realizan estudios de simulación extensivos para evaluar el desempeño de los estimadores bajo distintos escenarios. Las aplicaciones a datos reales, incluyendo prevalencia de trastornos de salud mental e indicadores jurimétricos, ilustran la adecuación e interpretabilidad del marco Simplex bivariado propuesto.
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