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Biometrika 1974 61(2):277-283; doi:10.1093/biomet/61.2.277
© 1974 by Biometrika Trust
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A Wiener-Hopf integral equation arising in some inference and queueing problems

C. ATKINSON

Department of Mathematics, Imperial College London

The solution is presented to an integral equation of Wiener-Hopf type which has been recently treated numerically by Hinkley in connexion with the problem of inference about the change-point in a sequence of random variables. The closed form solution given here enables results to be obtained easily in situations where the numerical method fails. A similar integral equation arises in a queueing problem where the difference between inter-arrival and service time of a customer is distributed normally. Explicit expressions are derived for this situation also.

Key Words: Change-point • Inference • Queues • Wiener-Hopf integral equation


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