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Biometrika 1964 51(3-4):399-404; doi:10.1093/biomet/51.3-4.399
© 1964 by Biometrika Trust
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The statistics of a particular non-homogeneous Poisson process

D. M. WILLIS *

D.S.I.R., Radio Research Station Ditton Park, Slough, Bucks

An analytic expression is derived for the average probability density function of the time interval between two consecutive events in a continuum of time, for the case in which the instantaneous rate of occurrence of events contains a term varying sinusoidally with the time in addition to a constant term. Expressions are obtained also for the average values of the mean and variance of the time interval between two consecutiveevents. An application of the theory to the analysis of phenomena for which the data consist solely of the times of occurrence of isolated events in a continuum of time is discussed briefly.


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