Gumbel's Type I Bivariate Distribution Family Function
Estimate the association parameter of Gumbel's Type I bivariate distribution by maximum likelihood estimation.
bigumbelIexp(lapar = "identitylink", iapar = NULL, imethod = 1)
lapar |
Link function applied to the association parameter
alpha.
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 |
The cumulative distribution function is
P(Y1 <= y1, Y2 <= y2) = exp(-y1-y2+alpha*y1*y2) + 1 - exp(-y1) - exp(-y2)
for real alpha. The support of the function is for y1>0 and y2>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.
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 1. This is because each marginal distribution corresponds to a exponential distribution with unit mean.
This VGAM family function should be used with caution.
T. W. Yee
Gumbel, E. J. (1960). Bivariate Exponential Distributions. Journal of the American Statistical Association, 55, 698–707.
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, data = gdata, trace = TRUE) coef(fit, matrix = TRUE) Coef(fit) head(fitted(fit))
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