¹University College London, Great Ormond Street Institute of Child Health, Population Policy and Practice Programme, London, United Kingdom. Miss. Email: e.koutoumanou@ucl.ac.uk
²University College London, Great Ormond Street Institute of Child Health, Population Policy and Practice Programme, London, United Kingdom. PhD. Email: a.wade@ucl.ac.uk
³University College London, Great Ormond Street Institute of Child Health, Population Policy and Practice Programme, London, United Kingdom. PhD. Email: m.cortina@ucl.ac.uk

The local dependence function (LDF) describes changes in the correlation structure of continuous bivariate random variables along their range. Bivariate density functions with Beta marginals can be used to model jointly a wide variety of data with bounded outcomes in the (0,1) range, e.g. proportions. In this paper we obtain expressions for the LDF of bivariate densities constructed using three different copula models (Frank, Gumbel and Joe) with Beta marginal distributions, present examples for each, and discuss an application of these models to analyse data collected in a study of marks obtained on a statistics exam by postgraduate students.

Key words: Association, Beta distribution, Bivariate distribution, Copula, Correlation.

La función de dependencia local (FDL) describe cambios en la estructura de la correlación entre dos variables aleatorias continuas sobre su recorrido conjunto. Funciones bivariadas de densidad de probabilidad con densidades marginales Beta pueden utilizarse apar modelar conjuntamente una amplia variedad de variables respuesta acotadas en el intervalo (0, 1), por ejemplo proporciones.
En este artículo obtenemos expresiones para la FDL de densidades bivariadas utilizando tres modelos de cópulas (Frank, Gumbel y Joe) con densidades marginales Beta, presentamos ejemplos para cada una de estas funciones, y discutimos una aplicación de estos modelos al an{a}lisis de datos recolectados en un estudio de calificaciones para un examen de estadística aplicado a estudiantes de postgrado.

Palabras clave: asociación, distribución Beta, cópula, correlación, función de distribución bivariada.

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