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## Modelagem em análise de sobrevivência para dados médicos bivariados utilizando funções cópulas e fração de cura; Modeling in survival analysis for medical data using bivariate copula functions and cure fraction.

Barros, Emilio Augusto Coelho
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Tese de Doutorado Formato: application/pdf
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## Conditional expectation formulae for copulas

Crane, G.; Van Der Hoek, J.
Fonte: Blackwell Publ Ltd Publicador: Blackwell Publ Ltd
Tipo: Artigo de Revista Científica
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Not only are copula functions joint distribution functions in their own right, they also provide a link between multivariate distributions and their lower-dimensional marginal distributions. Copulas have a structure that allows us to characterize all possible multivariate distributions, and therefore they have the potential to be a very useful statistical tool. Although copulas can be traced back to 1959, there is still much scope for new results, as most of the early work was theoretical rather than practical. We focus on simple practical tools based on conditional expectation, because such tools are not widely available. When dealing with data sets in which the dependence throughout the sample is variable, we suggest that copula-based regression curves may be more accurate predictors of specific outcomes than linear models. We derive simple conditional expectation formulae in terms of copulas and apply them to a combination of simulated and real data.; Glenis J. Crane and John van der Hoek; © 2008 Australian Statistical Publishing Association Inc.

## A new bivariate extension of FGM copulas

Amblard, Cécile; Girard, Stéphane
Tipo: Artigo de Revista Científica
We show an analytic method to construct a bivariate distribution function (DF) with given marginal distributions and correlation coefficient. We introduce a convenient mathematical tool, called a copula, to connect two DFs with any prescribed dependence structure. If the correlation of two variables is weak (Pearson's correlation coefficient $|\rho| <1/3$), the Farlie-Gumbel-Morgenstern (FGM) copula provides an intuitive and natural way for constructing such a bivariate DF. When the linear correlation is stronger, the FGM copula cannot work anymore. In this case, we propose to use a Gaussian copula, which connects two given marginals and directly related to the linear correlation coefficient between two variables. Using the copulas, we constructed the BLFs and discuss its statistical properties. Especially, we focused on the FUV--FIR BLF, since these two luminosities are related to the star formation (SF) activity. Though both the FUV and FIR are related to the SF activity, the univariate LFs have a very different functional form: former is well described by the Schechter function whilst the latter has a much more extended power-law like luminous end. We constructed the FUV-FIR BLFs by the FGM and Gaussian copulas with different strength of correlation...