From: Spencer Graves <spencer.graves_at_pdf.com>

Date: Fri, 21 Mar 2008 10:34:05 -0700

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 Fri 21 Mar 2008 - 17:41:17 GMT

Date: Fri, 21 Mar 2008 10:34:05 -0700

Hi, All:

- My previous email on this subject seemed to contain an error; check the correction below; please excuse my errors.

Is there a function in R to compute the expected range of a sample of size n from some distribution? I ask, because I was recently asked about the control chart constant 'd2', which is the expected range for a sample of size n from a standard normal.

There is a fairly simple formula for the expected value of the
range, given, e.g., in Kendall and Stuart (1969) The Advanced Theory of
Statistics, vol. 1, Distribution Theory, 3rd ed. (Hafner, expression

(14.82), sec. 14.25: The exact distribution of the range, p. 339).

Unfortunately, either I don't understand this formula, or it's wrong.
Using expression (14.1) in the same reference, I get the following:

E(R) = n*integral{-Inf to Inf of x*[(F(x))**(n-1) -

(1-F(x))**(n-1)]*dF(x).

Thanks, Spencer Graves ______________________________________________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 Fri 21 Mar 2008 - 17:41:17 GMT

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