inv.chisqff: Inverse Chi-squared Distribution.
In VGAMextra: Additions and Extensions of the 'VGAM' Package

inv.chisqff

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

link is the link function applied to the degrees of freedom, leading to the unique linear predictor in this family function. By default, the link is loglink.

zero allows to model the single linear predictor as intercept–only.

For further details, see CommonVGAMffArguments.

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.

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)

VGAMextra documentation built on Aug. 21, 2025, 5:57 p.m.