R: Ali-Mikhail-Haq Distribution Family Function

biamhcop {VGAM} | R Documentation

## Ali-Mikhail-Haq Distribution Family Function

### Description

Estimate the association parameter of Ali-Mikhail-Haq's bivariate distribution by maximum likelihood estimation.

### Usage

    biamhcop(lapar = "rhobitlink", iapar = NULL, imethod = 1, nsimEIM = 250)

### Arguments

`lapar` | Link function applied to the association parameter alpha, which is real and -1 < alpha < 1. See `Links` for more choices.
`iapar` | 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`.
`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 `iapar`.
`nsimEIM` | See `CommonVGAMffArguments` for more information.

### 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. This is an Archimedean copula.

### 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 and C. S. Chee

### References

Balakrishnan, N. and Lai, C.-D. (2009). Continuous Bivariate Distributions, 2nd ed. New York: Springer.

### See Also

`rbiamhcop`, `bifgmcop`, `bigumbelIexp`, `rbilogis`, `simulate.vlm`.

### Examples

    ymat <- rbiamhcop(1000, apar = rhobitlink(2, inverse = TRUE))
    fit <- vglm(ymat ~ 1, biamhcop, trace = TRUE)
    coef(fit, matrix = TRUE)
    Coef(fit)

[Package VGAM version 1.1-3 Index]