

   TThhee FF DDiissttrriibbuuttiioonn

        df(x, df1, df2)
        pf(q, df1, df2, ncp=0)
        qf(p, df1, df2)
        rf(n, df1, df2)

   AArrgguummeennttss::

        x,q: vector of quantiles.

          p: vector of probabilities.

          n: number of observations to generate.

    df1,df2: degrees of freedom.

        ncp: non-centrality parameter.

   VVaalluuee::

        These functions provide information about the F distri-
        bution with `df1' and `df2' degrees of freedom (and
        optional non-centrality parameter `ncp').  `df' gives
        the density, `pf' gives the distribution function `qf'
        gives the quantile function and `rf' generates random
        deviates.

        The F distribution with `df1 =' n1 and `df2 =' n2
        degrees of freedom has density

         f(x) = Gamma((n1 + n2)/2) / (Gamma(n1/2) Gamma(n2/2))
         (n1/n2)^(n1/2) x^(n1/2 - 1)
         (1 + (n1/n2) x)^-(n1 + n2)/2

        for x > 0.

   SSeeee AAllssoo::

        `dt' for Student's t distribution, the square of which
        is (almost) equivalent to the F distribution with `df2'
        = 1.

   EExxaammpplleess::

        df(1,1,1) == dt(1,1)# TRUE

        ## Identity:  qf(2*p -1, 1, df)) == qt(p, df)^2)  for  p >= 1/2
        p <- seq(1/2, .99, length=50); df <- 10
        rel.err <- function(x,y) ifelse(x==y,0, abs(x-y)/mean(abs(c(x,y))))
        quantile(rel.err(qf(2*p -1, df1=1, df2=df), qt(p, df)^2), .90)# ~= 7e-9

