VGAM (version 0.7-3)

fff: F Distribution Family Function

Description

Maximum likelihood estimation of the (2-parameter) F distribution.

Usage

fff(link="loge", earg=list(), idf1=NULL, idf2=NULL,
    method.init=1, zero=NULL)

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.

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.

References

Evans, M., Hastings, N. and Peacock, B. (2000) Statistical Distributions, New York: Wiley-Interscience, Third edition.

See Also

FDist.

Examples

x = runif(n <- 4000)
df1 = exp(2+0.5*x)
df2 = exp(2-0.5*x)
y = rf(n, df1, df2)
fit = vglm(y  ~ x, fff, trace=TRUE)
fit = vglm(y  ~ x, fff(link="logoff", earg=list(offset=0.5)), trace=TRUE)
coef(fit, matrix=TRUE)
Coef(fit)
vcov(fit)   # caution needed!