1Universidad Autónoma Metropolitana Unidad Iztapalapa, Departamento de Matemáticas, Ciudad de México, México. Profesor investigador. Email: ge@xanum.uam.mx
2Universidad Autónoma Metropolitana Unidad Iztapalapa, Departamento de Matemáticas, Ciudad de México, México. Estudiante de doctorado. Email: cbi206280113@xanum.uam.mx
Las cópulas se han convertido en una herramienta útil para el modelado multivariado tanto estocástico como estadístico. En este artículo se revisan propiedades fundamentales de las cópulas que permitan caracterizar la estructura de dependencia de familias de distribución bivariadas definidas por la cópula. También se describen algunas clases de cópulas, enfatizando en la importancia de la cópula Gaussiana y la familia Arquimediana. Se resalta la utilidad de las cópulas para el modelado de parejas de variables aleatorias continuas y el de las discretas. La aplicación de la cópula se ilustra con la construcción de modelos de regresión de Markov de primer orden para respuestas no Gaussianas.
Palabras clave: dependencia, cópula, medida de asociación, estadísticaaplicada, τ de Kendall, ρ de Spearman, correlaciónserial.
Copulas have become a useful tool for the multivariate modelling in both stochastics and statistics. In this article, fundamental properties that allow the characterization of the dependence structure of families of the bivariate distributions defined by the copula are reviewed. Also, the importance of both the Gaussian copula and the Archimedean family is emphasized while some classes of copulas are described. The usefulness for modelling either discrete or continuous random couples is highlighted. The construction of first-order Markov regression models for non-Gaussian responses illustrates the application of the copula.
Key words: Dependence, Copula, Measure of association, Appliedstatistics, Kendall τ, Spearman ρ, Serial correlation.
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Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:
@ARTICLE{RCEv32n1a03,
AUTHOR = {Escarela, Gabriel and Hernández, Angélica},
TITLE = {{Modelado de parejas aleatorias usando cópulas}},
JOURNAL = {Revista Colombiana de Estadística},
YEAR = {2009},
volume = {32},
number = {1}, ]]>
pages = {33-58}
}