Why do the integration in Excel instead of using the integrate function in R?  The R function will allow integration from -Inf to Inf.
 
What was the correction to the formula?  The last one you showed  looked like the difference between the average min and average max, but did not take into account the correlation between the max and min (going from memory, don't have my theory books handy). For large n the correlation is probably small enough that it makes a good approximation. 

________________________________

From: Spencer Graves [mailto:spencer.graves@pdf.com]
Sent: Fri 3/21/2008 3:39 PM
To: Greg Snow
Cc: r-help@r-project.org
Subject: Re: [R] function for the average or expected range?; CORECTION



Hi, Greg:

      Thanks very much for the reply.

      1.  The 'ptukey' and 'qtukey' function are the distribution of the
studentized range, not the range.  I tried "sum(ptukey(x, 2, df=Inf,
lower=FALSE))*.1" and got 1.179 vs. 1.128 in the standard table of d2
for n = 2 observations per subgroup.

      2.  I tried simulation and found that I needed 1e7 or 1e8 random
normal deviates to get the accuracy of the published table.

      3.  Then I programmed in Excel the integral over seq(-5, 5, .1)
using a correction to the formula I got from Kendall and Stuart and got
the exact numbers in the published table except in one case where it was
off by 1 in the last significant digit.

      Thanks again,
      Spencer

Greg Snow wrote:
> The "ptukey" and "qtukey" functions may be what you want (or at least in
> the right direction).
>
> You could also easily estimate this by simulation.
>
> Hope this helps,
>
>  



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