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

[Spencer Graves]

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 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,
> >
> >  
>