# bifgmcop: Farlie-Gumbel-Morgenstern's Bivariate Distribution Family... In VGAM: Vector Generalized Linear and Additive Models

 bifgmcop R Documentation

## 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 = "rhobitlink", iapar = NULL, imethod = 1)


### Arguments

 lapar, iapar, imethod Details at CommonVGAMffArguments. See Links for more link function choices.

### 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.

### Value

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

### Note

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

### References

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 Statisticsâ€”Theory and Methods, 36(12), 2213â€“2222.

rbifgmcop, bifrankcop, bifgmexp, simulate.vlm.

### Examples

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)
Coef(fit)