biamhcop.RdEstimate 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 $$P(Y_1 \leq y_1, Y_2 \leq y_2) = y_1 y_2 / ( 1 - \alpha (1 - y_1) (1 - y_2) ) $$ 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.
An object of class "vglmff"
(see vglmff-class).
The object is used by modelling functions
such as vglm
and vgam.
Balakrishnan, N. and Lai, C.-D. (2009). Continuous Bivariate Distributions, 2nd ed. New York: Springer.
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.
ymat <- rbiamhcop(1000, apar = rhobitlink(2, inverse = TRUE))
fit <- vglm(ymat ~ 1, biamhcop, trace = TRUE)
#> Iteration 1: loglikelihood = 51.436617
#> Iteration 2: loglikelihood = 51.438348
#> Iteration 3: loglikelihood = 51.438356
#> Iteration 4: loglikelihood = 51.438356
coef(fit, matrix = TRUE)
#> rhobitlink(apar)
#> (Intercept) 1.850311
Coef(fit)
#> apar
#> 0.7283273