[R] function for the average or expected range?

From: Spencer Graves <spencer.graves_at_pdf.com>
Date: Fri, 21 Mar 2008 09:14:50 -0700

Hi, All:

      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).:

     E(R) = integral{-Inf to Inf of [1 - (F(x))^n - (1-F(x))2] dx.

      Spencer Graves

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