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 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,