fff {VGAM} | R Documentation |
F Distribution Family Function
Description
Maximum likelihood estimation of the (2-parameter) F distribution.
Usage
fff(link = "loglink", idf1 = NULL, idf2 = NULL, nsimEIM = 100,
imethod = 1, zero = NULL)
Arguments
link |
Parameter link function for both parameters.
See |
idf1 , idf2 |
Numeric and positive. Initial value for the parameters. The default is to choose each value internally. |
nsimEIM , zero |
See |
imethod |
Initialization method. Either the value 1 or 2.
If both fail try setting values for
|
Details
The F distribution is named after Fisher and has
a density function
that has two parameters, called df1
and df2
here.
This function treats these degrees of freedom
as positive reals
rather than integers.
The mean of the distribution is
df2/(df2-2)
provided df2>2
,
and its variance is
2 df2^2 (df1+df2-2)/(df1 (df2-2)^2 (df2-4))
provided df2>4
.
The estimated mean is returned as the fitted values.
Although the F distribution can be defined to accommodate a
non-centrality parameter ncp
, it is assumed zero here.
Actually it shouldn't be too difficult to handle any known
ncp
; something to do in the short future.
Value
An object of class "vglmff"
(see vglmff-class
).
The object is used by modelling functions
such as vglm
and vgam
.
Warning
Numerical problems will occur when the estimates of the parameters are too low or too high.
Author(s)
T. W. Yee
References
Forbes, C., Evans, M., Hastings, N. and Peacock, B. (2011). Statistical Distributions, Hoboken, NJ, USA: John Wiley and Sons, Fourth edition.
See Also
Examples
## Not run:
fdata <- data.frame(x2 = runif(nn <- 2000))
fdata <- transform(fdata, df1 = exp(2+0.5*x2),
df2 = exp(2-0.5*x2))
fdata <- transform(fdata, y = rf(nn, df1, df2))
fit <- vglm(y ~ x2, fff, data = fdata, trace = TRUE)
coef(fit, matrix = TRUE)
## End(Not run)