Spencer Graves
2008-Mar-21 17:34 UTC
[R] function for the average or expected range?; CORECTION TO CORRECTION
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