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

From: Greg Snow <Greg.Snow_at_imail.org>
Date: Fri, 21 Mar 2008 13:45:27 -0600

You could also easily estimate this by simulation.

Hope this helps,

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

> -----Original Message-----
> From: r-help-bounces_at_r-project.org
> [mailto:r-help-bounces@r-project.org] On Behalf Of Spencer Graves

> Sent: Friday, March 21, 2008 11:13 AM
> To: r-help_at_r-project.org
> Subject: [R] function for the average or expected range?; CORECTION
>
> Hi, All:
>
> ** My previous email on this subject seemed to contain an
> error;  check the correction:
>
>       Is there a function in R to compute the expected range
> of a sample of size n from some distribution?  I ask, because
> 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 [(F(x))**(n-1) -
> (1-F(x))**(n-1)]dF(x).
>
>       Thanks,
>       Spencer Graves
>
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> and provide commented, minimal, self-contained, reproducible code.
>

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