Multiple Runs Distributions: Recurrences and Critical Values

Abstract Most traditional applications of runs tests have entailed bivariate runs distributions. Extensions to more general runs tests for randomness have been hindered by the lack of exact critical values for distributions with more than two kinds of elements. Combinatorial recurrences that can be used to compute exact significance levels for small sample sizes are presented for runs distributions for ν ≥ 2 kinds of elements. Critical values for small sample sizes are tabled for ν = 2(1)6. More extensive tables are available from the author.