A note on conjugate distributions for copulas

Abstract

A family of conjugated distributions for a given type of copulas is defined in this paper. Those copulas can be written as a mixture of d-dimensional parameter exponential functions. The generalized Farlie-Gumbel-Morgenstern copula is an example of this representation. This family is used to illustrate the estimation technique with real data. Also, the applicability of Bayesian predictive approach is shown in an education policy issue by defining goals for the number of students per class that leads to improve their performance at school.

A copula-based consistency analysis of education indicators

“…More precisely, if we have observed high failure rates, we see how they affect the probability of high rates of students below the baseline and how those high failure rates impact in the mean value of rates of students below the baseline. The ACS family has already shown a good performance in applications in the area, see for example [2] and [3]. It is also compatible with our data which, as we shall see, shows very low correlation.…”

“…We also observe that the complexity of the parametric space H (see Definition 3.1) could hinder the use of an informative prior distribution without a very solid base. About literature linking copula's theory and Bayesian estimation, see [6] and [3]. The Bayesian estimates of a and b, under quadratic loss function, for each year are shown in Table 2.…”

A method for the elicitation of copulas

“…For details on the properties of the copulas C 1 and C 2 , see specific literature Lai and Xie [12] and Rodríguez-Lallena and Úbeda-Flores [5]. We can also see the use of these models in practice in Fernández et al [15]. Define f 1 ðuÞ ¼ k 1 u a 1 ð1 À uÞ, f 2 ðvÞ ¼ k 2 v a 2 ð1 À vÞ, g i ðtÞ ¼ t bi ð1 À tÞ; i = 1, 2.…”