Algorithm AS 177: Expected Normal Order Statistics (Exact and Approximate)
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Abstract
DESCRIPTION AND PURPOSE The algorithms NSCOR1 and NSCOR2 calculate the expected values of normal order statistics in exact or approximate form respectively. NSCOR2 requires little storage and is fast, and hence is suitable for implementation on small computers or certain programmable calculators (HP-67, etc). This is not recommended for NSCOR1. Expected normal order statistics are needed in the calculation of analysis of variance tests of normality, such as W (Shapiro and Wilk, 1965) and W' (Shapiro and Francia, 1972). In a sample of size n the expected value of the rth largest order statistic is given by