Open Access
March, 1946 Distribution of Sample Arrangements for Runs Up and Down
P. S. Olmstead
Ann. Math. Statist. 17(1): 24-33 (March, 1946). DOI: 10.1214/aoms/1177731019


Using the notation of Levene and Wolfowitz [1], a new recursion formula is used to give the exact distribution of arrangements of $n$ numbers, no two alike, with runs up or down of length $p$ or more. These are tabled for $n$ and $p$ through $n = 14$. An exact solution is given for $p \geq n/2$. The average and variance determined by Levene and Wolfowitz are presented in a simplified form. The fraction of arrangements of $n$ numbers with runs of length $p$ or more are presented for the exact distributions, for the limiting Poisson Exponential, and for an extrapolation from the exact distributions. Agreement among the tables is discussed.


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P. S. Olmstead. "Distribution of Sample Arrangements for Runs Up and Down." Ann. Math. Statist. 17 (1) 24 - 33, March, 1946.


Published: March, 1946
First available in Project Euclid: 28 April 2007

zbMATH: 0063.06035
MathSciNet: MR15692
Digital Object Identifier: 10.1214/aoms/1177731019

Rights: Copyright © 1946 Institute of Mathematical Statistics

Vol.17 • No. 1 • March, 1946
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