bifgmcop: Farlie-Gumbel-Morgenstern's Bivariate Distribution Family...

View source: R/family.bivariate.R

bifgmcopR Documentation

Farlie-Gumbel-Morgenstern's Bivariate Distribution Family Function


Estimate the association parameter of Farlie-Gumbel-Morgenstern's bivariate distribution by maximum likelihood estimation.


bifgmcop(lapar = "rhobitlink", iapar = NULL, imethod = 1)


lapar, iapar, imethod

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


The cumulative distribution function is

P(Y_1 \leq y_1, Y_2 \leq y_2) = y_1 y_2 ( 1 + \alpha (1 - y_1) (1 - y_2) )

for -1 < \alpha < 1. The support of the function is the unit square. The marginal distributions are the standard uniform distributions. When \alpha = 0 the random variables are independent.


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 0.5. This is because each marginal distribution corresponds to a standard uniform distribution.


T. W. Yee


Castillo, E., Hadi, A. S., Balakrishnan, N. and Sarabia, J. S. (2005). Extreme Value and Related Models with Applications in Engineering and Science, Hoboken, NJ, USA: Wiley-Interscience.

Smith, M. D. (2007). Invariance theorems for Fisher information. Communications in Statistics—Theory and Methods, 36(12), 2213–2222.

See Also

rbifgmcop, bifrankcop, bifgmexp, simulate.vlm.


ymat <- rbifgmcop(1000, apar = rhobitlink(3, inverse = TRUE))
## Not run: plot(ymat, col = "blue")
fit <- vglm(ymat ~ 1, fam = bifgmcop, trace = TRUE)
coef(fit, matrix = TRUE)

VGAM documentation built on Sept. 19, 2023, 9:06 a.m.