VGAM (version 1.0-4)

# bifgmcop: Farlie-Gumbel-Morgenstern's Bivariate Distribution Family Function

## Description

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

## Usage

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

## Arguments

lapar, iapar, imethod

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

## Value

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

## Details

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.

## References

Castillo, E., Hadi, A. S., Balakrishnan, N. 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.

rbifgmcop, bifrankcop, bifgmexp, simulate.vlm.

## Examples

Run this code
# NOT RUN {
ymat <- rbifgmcop(n = 1000, apar = rhobit(3, inverse = TRUE))
# }
# NOT RUN {
plot(ymat, col = "blue")
# }
# NOT RUN {
fit <- vglm(ymat ~ 1, fam = bifgmcop, trace = TRUE)
coef(fit, matrix = TRUE)
Coef(fit)