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Sums of ordered intervals and distances

Published online by Cambridge University Press:  26 February 2010

D. E. Barton  and
F. N. David
D. E. Barton
Affiliation:
Department of Statistics, University College, London.
F. N. David
Affiliation:
Department of Statistics, University College, London.
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Extract

The analysis of the intervals which arise between events occurring randomly in time is a problem which is both interesting and important statistically. Two distinct types of data may arise: either the period of time during which the events are observed may be fixed or the number of intervals may be fixed. It may happen that the intervals between pairs of events, close in time, cannot be accurately measured. It is thus necessary to consider the lengths of intervals ordered according to their magnitudes. We derive here functions of these ordered interval lengths which may be used as a basis for tests for randomness of events occurring in a fixed period of time. The mathematical formulation of this problem is in terms of the classical problem of intervals between points on a line.

Type
Research Article
Information
Mathematika , Volume 2 , Issue 2 , December 1955 , pp. 150 - 159
Copyright
Copyright © University College London 1955

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References

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