Runs Determined in a Sample by an Arbitrary Cut

This payer, after making a critical review of the literature 'pertaining to runs above and below in a fixed sample, provides the following extensions: 1. Sample arrangement distributions for runs of length at least s on one, each, and either side of any selected cut for samples of 10 and 20, 2. Sample arrangement distributions for runs of length at least s on one, each, and either side of the median for saynples of 10, 20, 40, 60, 100, and 200, 3. Sample arrangement distributions for runs of length at least s on each side of all possible cuts for samples of 10, 20, Jfi, and 100, 4. Asymptotic values of the probabilities of such arrangements when the sample size and length of run are large, 5. Convenient charts and tables for probabilities of 0.01, 0.10, 0.50, 0.90, and 0.99 to facilitate use by engineers and scientists, and 6. Discussion of a simple application. The inclusion of the case for runs of length at least s on each side of all possible cuts should prove very useful because it provides a quantitative measure for a common operational procedure for which the exact probabilities were heretofore unknown.