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)
lapar |
Link function applied to the association parameter
alpha, which is real
and -1 < alpha < 1.
See |
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 |
An integer with value |
nsimEIM |
See |
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.
ymat <- rbiamhcop(1000, apar = rhobitlink(2, inverse = TRUE)) fit <- vglm(ymat ~ 1, biamhcop, trace = TRUE) coef(fit, matrix = TRUE) Coef(fit)
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