# fff: F Distribution Family Function In VGAM: Vector Generalized Linear and Additive Models

## Description

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

## Usage

 ```1 2``` ```fff(link = "loglink", idf1 = NULL, idf2 = NULL, nsimEIM = 100, imethod = 1, zero = NULL) ```

## Arguments

 `link` Parameter link function for both parameters. See `Links` for more choices. The default keeps the parameters positive. `idf1, idf2` Numeric and positive. Initial value for the parameters. The default is to choose each value internally. `nsimEIM, zero` See `CommonVGAMffArguments` for more information. `imethod` Initialization method. Either the value 1 or 2. If both fail try setting values for `idf1` and `idf2`.

## 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.

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.

`FDist`.
 ```1 2 3 4 5 6 7 8 9``` ```## 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) ```