R: F Distribution Family Function

fff {VGAM} | R Documentation

## F Distribution Family Function

### Description

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

### Usage

    fff(link = "loge", 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.

### 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

`FDist`.

### 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)

[Package VGAM version 1.0-3 Index]