biamhcop: Ali-Mikhail-Haq Distribution Family Function

View source: R/family.bivariate.R

biamhcopR Documentation

Ali-Mikhail-Haq Distribution Family Function


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


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



Link function applied to the association parameter alpha, which is real and -1 < alpha < 1. See Links for more choices.


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.


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.


See CommonVGAMffArguments for more information.


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.


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


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 and C. S. Chee


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

See Also

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


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

VGAM documentation built on July 6, 2022, 5:05 p.m.