inv.chisqff  R Documentation 
Maximum likelihood estimation of the degrees of freedom for an inverse chi–squared distribution using Fisher scoring.
inv.chisqff(link = "loglink", zero = NULL)
link, zero 
For further details, see

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.
An object of class "vglmff"
.
See vglmffclass
for further details.
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.
As with chisq
or
Chisquare
, the degrees of freedom are
non–negative but allowed to be non–integer.
V. Miranda.
loglink
,
CommonVGAMffArguments
,
inv.chisqMlink
,
zero
.
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)
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