

   TThhee SSttuuddeennttiizzeedd RRaannggee DDiissttrriibbuuttiioonn

        ptukey(q, nmeans, df, nranges = 1)
        qtukey(p, nmeans, df, nranges = 1)

   AArrgguummeennttss::

          q: vector of quantiles.

          p: vector of probabilities.

     nmeans: sample size for range (same for each group).

         df: degrees of freedom for s (see below).

    nranges: number of groups whose maximum range is consid-
             ered.

   DDeessccrriippttiioonn::

        These functions provide information about the distribu-
        tion of the studentized range, R/s, where R is the
        range of a standard normal sample of size n and s^2 is
        independently distributed as chi-squared with df
        degrees of freedom, see `pchisq'.

        If ng =`nranges' is greater than one, R is the maximum
        of ng groups of `nmeans' observations each.

   VVaalluuee::

        `ptukey' gives the distribution function and `qtukey'
        its inverse, the quantile function.

   NNoottee::

        A Legendre 16-point formula is used for the integral of
        `ptukey'.  The computations are relatively expensive,
        especially for `qtukey' which uses a simple secant
        method for finding the inverse of `ptukey'.
        `qtukey(..)' will be accurate to the 4th decimal place.

   RReeffeerreenncceess::

        Copenhaver, Margaret Diponzio & Holland, Burt S.
        (1988).
        Multiple comparisons of simple effects in the two-way
        analysis of variance with fixed effects.  Journal of
        Statistical Computation and Simulation, 30, 1-15.

   SSeeee AAllssoo::

        `pnorm' and `qnorm' for the corresponding functions for
        the normal distribution.

   EExxaammpplleess::

        system.time(curve(ptukey(x, nm=6, df=5), from=-1, to=8, n=101))
        (ptt <- ptukey(0:10, 2, df= 5))
        (qtt <- qtukey(.95, 2, df= 2:11))
        ## The precision may be not much more than about 8 digits:
        summary(abs(.95 - ptukey(qtt,2, df = 2:11)))

