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

bifgmcop {VGAM} | 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 = "rhobit", 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(Y1 <= y1, Y2 <= y2) = y1 * y2 * ( 1 + alpha * (1 - y1) * (1 - y2) )

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.

### Author(s)

T. W. Yee

### 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.

### See Also

`rbifgmcop`, `bifrankcop`, `bifgmexp`, `simulate.vlm`.

### Examples

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

[Package VGAM version 1.0-3 Index]