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VGAM (version 1.0-6)

bistudentt: Bivariate Student-t Family Function

Description

Estimate the degrees of freedom and correlation parameters of the (bivariate) Student-t distribution by maximum likelihood estimation.

Usage

bistudentt(ldf = "loglog", lrho = "rhobit",
           idf = NULL, irho = NULL, imethod = 1,
           parallel = FALSE, zero = "rho")

Arguments

ldf, lrho, idf, irho, imethod

Details at CommonVGAMffArguments. See Links for more link function choices.

parallel, zero

Value

An object of class "vglmff" (see vglmff-class). The object is used by modelling functions such as vglm and vgam.

Warning

The working weight matrices have not been fully checked.

Details

The density function is $$f(y_1, y_2; \nu, \rho) = \frac{1}{2\pi\sqrt{1-\rho^2}} (1 + y_1^2 + y_2^2 - 2\rho y_1 y_2) / (\nu (1-\rho^2))^{(\nu+2)/2} $$ for \(-1 < \rho < 1\), and real \(y_1\) and \(y_2\).

This VGAM family function can handle multiple responses, for example, a six-column matrix where the first 2 columns is the first out of three responses, the next 2 columns being the next response, etc.

References

Schepsmeier, U. and Stober, J. (2013) Derivatives and Fisher information of bivariate copulas. Statistical Papers.

See Also

dbistudentt, binormal, pt.

Examples

Run this code
# NOT RUN {
nn <- 1000
mydof <- loglog(1, inverse = TRUE)
ymat <- cbind(rt(nn, df = mydof), rt(nn, df = mydof))
bdata <- data.frame(y1 = ymat[, 1], y2 = ymat[, 2],
                    y3 = ymat[, 1], y4 = ymat[, 2], x2 = runif(nn))
summary(bdata)
# }
# NOT RUN {
 plot(ymat, col = "blue") 
# }
# NOT RUN {
fit1 <- vglm(cbind(y1, y2, y3, y4) ~ 1,  # 2 responses, e.g., (y1,y2) is the 1st
             fam = bistudentt,  # crit = "coef",  # Sometimes a good idea
             data = bdata, trace = TRUE)

coef(fit1, matrix = TRUE)
Coef(fit1)
head(fitted(fit1))
summary(fit1)
# }

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