bigumbelIexp {VGAM} | R Documentation |
Gumbel's Type I Bivariate Distribution Family Function
Description
Estimate the association parameter of Gumbel's Type I bivariate distribution by maximum likelihood estimation.
Usage
bigumbelIexp(lapar = "identitylink", iapar = NULL, imethod = 1)
Arguments
lapar |
Link function applied to the association parameter
|
iapar |
Numeric. Optional initial value for |
imethod |
An integer with value |
Details
The cumulative distribution function is
P(Y_1 \leq y_1, Y_2 \leq y_2) = e^{-y_1-y_2+\alpha y_1 y_2}
+ 1 - e^{-y_1} - e^{-y_2}
for real \alpha
.
The support of the function is for y_1>0
and
y_2>0
.
The marginal distributions are an exponential distribution with
unit mean.
A variant of Newton-Raphson is used, which only seems
to work for an intercept model.
It is a very good idea to set trace=TRUE
.
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 1. This is because each marginal distribution corresponds to a exponential distribution with unit mean.
This VGAM family function should be used with caution.
Author(s)
T. W. Yee
References
Gumbel, E. J. (1960). Bivariate Exponential Distributions. Journal of the American Statistical Association, 55, 698–707.
See Also
Examples
nn <- 1000
gdata <- data.frame(y1 = rexp(nn), y2 = rexp(nn))
## Not run: with(gdata, plot(cbind(y1, y2)))
fit <- vglm(cbind(y1, y2) ~ 1, bigumbelIexp, gdata, trace = TRUE)
coef(fit, matrix = TRUE)
Coef(fit)
head(fitted(fit))