The Probability Integral of Range for Samples from a Symmetrical Unimodal Population

Abstract

An asymptotic expression is given for the probability integral of range for samples from a symmetrical unimodal population. Its accuracy is investigated for the case of a normal parent population and for sample sizes from 20 to 100. Over this range errors are small, and by using a correction based on values given below the probability integral can be found with a maximum error of 0.0001. Percentage points of range in the normal case are tabled for $n =$ 20, 40, 60, 80 and 100.