Distribution theory of runs via exchangeable random variables

Eugene F. Schuster

Statistics & Probability Letters, 1991, vol. 11, issue 5, 379-386

Abstract: The conditional distribution theory of the number of runs R in a randomly ordered sequence of length N = m + n of two types of symbols, say m of type F (failures) and n of type S (successes), is studied via the representation R = 1 + [summation operator]m + 1k = 1[alpha]kIk where I1,..., Im + 1 are exchangeable Bernoulli random variables with [alpha]1 = [alpha]m + 1 = 1 and [alpha]k = 2, otherwise. This exchangeable representation of R, and related statistics, considerably facilitates the study of distribution theory of these statistics.

Keywords: Runs; test; longest; run; exchangeable; Pascal's; triangle; of; order; k (search for similar items in EconPapers)
Date: 1991
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