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XXII.—Some Distributions associated with a Randomly Arranged Set of Numbers

Published online by Cambridge University Press:  15 September 2014

W. O. Kermack  and
A. G. McKendrick
W. O. Kermack
Affiliation:
Laboratory of the Royal College of Physicians, Edinburgh
A. G. McKendrick
Affiliation:
Laboratory of the Royal College of Physicians, Edinburgh
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Extract

In the course of a search for criteria which would assist in deciding whether a particular series of numbers was randomly arranged, it was found necessary to investigate some of the more obvious characters of a random series of numbers. If the series is an infinite one and all the numbers are unequal (the series of decimals between o and 1 selected in some random fashion may be considered) certain of the numbers will be maximal, that is greater than their immediate neighbours, whilst others will be minimal, that is less than their immediate neighbours. Every maximal number is succeeded by a run down, that is by a series of descending numbers ending in the succeeding minimal number. The length of a run down is the number of numbers it contains, including the maximal number which begins it and the minimal number which ends it. The length of a run up is similarly defined. Clearly the minimum length of a run is 2.

Type
Proceedings
Information
Proceedings of the Royal Society of Edinburgh , Volume 57 , 1938 , pp. 332 - 376
Copyright
Copyright © Royal Society of Edinburgh 1938

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References

References to Literature

André, D., 1884. Ann. Sci. Éc. norm. sup., vol. i, p. 121.CrossRefGoogle Scholar
André, D., 1895. Journ. Math., vol. i, p. 315.Google Scholar
Kermack, W. O., and McKendrick, A. G., 1938. Proc. Roy. Soc. Edin., vol. lvii, pp. 228–240.CrossRefGoogle Scholar
MacMahon, P. A., 1915. Combinatory Analysis, vol. i, Camb. Univ. Press.Google Scholar
Netto, E., 1901. Lehrbuch der Combinatorik, Teubner, Leipzig.Google Scholar