bigumbelIexp: Gumbel's Type I Bivariate Distribution Family Function

View source: R/family.bivariate.R

bigumbelIexpR Documentation

Gumbel's Type I Bivariate Distribution Family Function


Estimate the association parameter of Gumbel's Type I bivariate distribution by maximum likelihood estimation.


bigumbelIexp(lapar = "identitylink", iapar = NULL, imethod = 1)



Link function applied to the association parameter alpha. See Links for more choices.


Numeric. Optional initial value for alpha. By default, an initial value is chosen internally. If a convergence failure occurs try assigning a different value. Assigning a value will override the argument imethod.


An integer with value 1 or 2 which specifies the initialization method. If failure to converge occurs try the other value, or else specify a value for ia.


The cumulative distribution function is

P(Y1 <= y1, Y2 <= y2) = exp(-y1-y2+alpha*y1*y2) + 1 - exp(-y1) - exp(-y2)

for real alpha. The support of the function is for y1>0 and y2>0. The marginal distributions are an exponential distribution with unit mean.

A variant of Newton-Raphson is used, which only seems to work for an intercept model. It is a very good idea to set trace=TRUE.


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


The response must be a two-column matrix. Currently, the fitted value is a matrix with two columns and values equal to 1. This is because each marginal distribution corresponds to a exponential distribution with unit mean.

This VGAM family function should be used with caution.


T. W. Yee


Gumbel, E. J. (1960). Bivariate Exponential Distributions. Journal of the American Statistical Association, 55, 698–707.

See Also



nn <- 1000
gdata <- data.frame(y1 = rexp(nn), y2 = rexp(nn))
## Not run:  with(gdata, plot(cbind(y1, y2))) 
fit <- vglm(cbind(y1, y2) ~ 1, bigumbelIexp, gdata, trace = TRUE)
coef(fit, matrix = TRUE)

VGAM documentation built on July 6, 2022, 5:05 p.m.