VGAM (version 1.0-4)

# biamhcop: 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 = "rhobit", 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.

## 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. This is an Archimedean copula.

## References

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

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

## Examples

Run this code
# NOT RUN {
ymat <- rbiamhcop(1000, apar = rhobit(2, inverse = TRUE))
fit <- vglm(ymat ~ 1, biamhcop, trace = TRUE)
coef(fit, matrix = TRUE)
Coef(fit)
# }


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