# Re: [R] function for the average or expected range?; CORECTION

From: Greg Snow <Greg.Snow_at_imail.org>
Date: Mon, 24 Mar 2008 10:22:27 -0600

Well it looks like you found your answer. Further the fact that my suggestions of possibilities did not help and the fact that noone else has chimed in would suggest that there is not any easier way to get your answer.

I was thinking that taking into account the correlation between the min and the max may give different answers than your formula, but so far my tests have not shown enough of a difference to matter. If you use this with a distribution rather than the normal, you may want to do a couple of simulations just to check, but otherwise your formula seems to be working fine.

Hope this helped,

```--
Gregory (Greg) L. Snow Ph.D.
Statistical Data Center
Intermountain Healthcare
greg.snow_at_imail.org
(801) 408-8111

> -----Original Message-----
> From: Spencer Graves [mailto:spencer.graves@pdf.com]

> Sent: Saturday, March 22, 2008 9:40 AM
> To: Greg Snow
> Cc: r-help_at_r-project.org
> Subject: Re: [R] function for the average or expected range?;
> CORECTION
>
> Hi, Greg:
>
>       1.  I did the integration in Excel for four reasons:
> First, it's easier (even for me) to see what's happening and
> debug for something that simple.  Second, my audience were
> people who were probably not R literate, and they could
> likely understand and use the Excel file easier than than an
> R script.  Third, my experience with the R 'integrate' has
> been less than satisfactory, especially when integrating from
> (-Inf) to Inf.  Finally, to check my work, I often program
> things like that first in Excel then in R.  If I get the same
> answer in both, I feel more confident in my R results.  I
> haven't programmed this result in R yet, but if I do, the
> fact that I already did it in Excel will make it easier for
> me to be confident of the answers.  The function
> "getParamerFun{qAnalyst}" gets the correct answer from n =
> 2:25 but returns wrong answers outside that range.
>
>
>       2.  I think the "CORRECTION TO CORRECTION" included a correct
> formula:
>
>            E(R) = n*integral{-Inf to Inf of x*[(F(x))**(n-1)
> - (1-F(x))**(n-1)]*dF(x).
>
>       The "CORRECTION" omitted the "x*".  The first version
>
>       Am I communicating?
>       Best Wishes,
>       Spencer
>
> Greg Snow wrote:
> > 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_at_pdf.com]
> > *Sent:* Fri 3/21/2008 3:39 PM
> > *To:* Greg Snow
> > *Cc:* r-help_at_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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