amh {VGAM}R Documentation

Ali-Mikhail-Haq Distribution Distribution Family Function

Description

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

Usage

amh(lalpha="rhobit", ealpha=list(), ialpha=NULL,
    method.init=1, nsimEIM=250)

Arguments

lalpha Link function applied to the association parameter alpha, which is real and -1 < alpha < 1. See Links for more choices.
ealpha List. Extra argument for the link. See earg in Links for general information.
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 method.init.
method.init 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 ialpha.
nsimEIM See CommonVGAMffArguments for more information.

Details

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.

Value

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

Note

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.

Author(s)

T. W. Yee and C. S. Chee

References

Hutchinson, T. P. and Lai, C. D. (1990) Continuous Bivariate Distributions, Emphasising Applications, Adelaide, South Australia: Rumsby Scientific Publishing.

See Also

ramh, fgm, gumbelIbiv.

Examples

ymat = ramh(1000, alpha=rhobit(2, inverse=TRUE))
fit = vglm(ymat ~ 1, amh, trace = TRUE)
coef(fit, mat=TRUE)
Coef(fit)

[Package VGAM version 0.7-7 Index]