amh {VGAM} | R Documentation |
Estimate the association parameter of Ali-Mikhail-Haq's bivariate distribution by maximum likelihood estimation.
amh(lalpha = "rhobit", ealpha = list(), ialpha = NULL, imethod = 1, nsimEIM = 250)
lalpha |
Link function applied to the association parameter
alpha, which is real
and -1 < alpha < 1.
See |
ealpha |
List. Extra argument for the link.
See |
ialpha |
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.
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.
ramh
,
fgm
,
gumbelIbiv
.
ymat <- ramh(1000, alpha = rhobit(2, inverse = TRUE)) fit <- vglm(ymat ~ 1, amh, trace = TRUE) coef(fit, matrix = TRUE) Coef(fit)