From: Spencer Graves <spencer.graves_at_pdf.com>

Date: Sat, 22 Mar 2008 08:40:27 -0700

R-help_at_r-project.org mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. Received on Sat 22 Mar 2008 - 15:43:29 GMT

Date: Sat, 22 Mar 2008 08:40:27 -0700

Hi, Greg:

- 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.
- 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 had many more problems.

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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