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The statistics of scaled random events

Published online by Cambridge University Press:  24 October 2008

R. O. Davies  and
J. W. Leech
R. O. Davies
Affiliation:
Queen Mary CollegeUniversity of LondonMile End RoadLondon, E. 1.
J. W. Leech
Affiliation:
Queen Mary CollegeUniversity of LondonMile End RoadLondon, E. 1.
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Abstract

When independent random events are scaled down by a factor n, the number of counts in a given time interval no longer obeys the Poisson Law. The correct distribution function is derived together with its moment-generating function and explicit formulae (n = 2, 4) for the first four moments about the mean. The theory is in agreement with experiments carried out with a scale-of-four counter. A more general treatment is given and is applied to find the variance for all even values of n.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 50 , Issue 4 , October 1954 , pp. 575 - 580
Copyright
Copyright © Cambridge Philosophical Society 1954

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References

REFERENCES

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