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Local dependence in bivariate copulae with Beta marginals
Dependencia local en copulas bivariadas con marginales Beta
DOI:
https://doi.org/10.15446/rce.v40n2.59404Keywords:
Beta distribution, local dependence function, copula, bivariate densities (en)Asociación, distribución Beta, cópula, correlación, función de distribución bivariada (es)
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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.
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 para 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 análisis de datos recolectados en un estudio de calificaciones para un examen de estadística aplicado a estudiantes de postgrado.
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1. Susanne Trick, Constantin A. Rothkopf, Frank Jäkel. (2023). Parameter estimation for a bivariate beta distribution with arbitrary beta marginals and positive correlation. METRON, 81(2), p.163. https://doi.org/10.1007/s40300-023-00247-2.
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