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.
Thanks,
Spencer Graves
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