| inv.chisqff {VGAMextra} | R Documentation |
Inverse Chi–squared Distribution.
Description
Maximum likelihood estimation of the degrees of freedom for an inverse chi–squared distribution using Fisher scoring.
Usage
inv.chisqff(link = "loglink", zero = NULL)
Arguments
link, zero |
For further details, see
|
Details
The inverse chi–squared distribution
with df = \nu \geq 0 degrees of
freedom implemented here has density
f(x; \nu) = \frac{ 2^{-\nu / 2} x^{-\nu/2 - 1}
e^{-1 / (2x)} }{ \Gamma(\nu / 2) },
where x > 0, and
\Gamma is the gamma function.
The mean of Y is 1 / (\nu - 2) (returned as the fitted
values), provided \nu > 2.
That is, while the expected information matrices used here are
valid in all regions of the parameter space, the regularity conditions
for maximum likelihood estimation are satisfied only if \nu > 2.
To enforce this condition, choose
link = logoff(offset = -2).
As with, chisq, the degrees of freedom are
treated as a parameter to be estimated using (by default) the
link loglink. However, the mean can also
be modelled with this family function.
See inv.chisqMlink
for specific details about this.
This family VGAM function handles multiple responses.
Value
An object of class "vglmff".
See vglmff-class for further details.
Warning
By default, the single linear/additive predictor in this family
function, say \eta = \log dof,
can be modeled in terms of covariates,
i.e., zero = NULL.
To model \eta as intercept–only set zero = "dof".
See zero for more details about this.
Note
As with chisq or
Chisquare, the degrees of freedom are
non–negative but allowed to be non–integer.
Author(s)
V. Miranda.
See Also
loglink,
CommonVGAMffArguments,
inv.chisqMlink,
zero.
Examples
set.seed(17010504)
dof <- 2.5
yy <- rinv.chisq(100, df = dof)
ics.d <- data.frame(y = yy) # The data.
fit.inv <- vglm(cbind(y, y) ~ 1, inv.chisqff,
data = ics.d, trace = TRUE, crit = "coef")
Coef(fit.inv)
summary(fit.inv)