Author(s)

James E. Marengo, Anne Marino Himes, W. Cade Reinberger, David L. Farnsworth

School of Mathematical Sciences, Rochester Institute of Technology, Rochester, USA.

The Inspection Paradox refers to the fact that in a Renewal Process, the length of the interarrival period which contains a fixed time is stochastically larger than the length of a typical interarrival period. To provide a more complete understanding of this phenomenon, conditioning arguments are used to obtain the distributions and moments of the lengths of the interarrival periods other than the one containing this fixed time for the case of the time-homogeneous Poisson Process. Distributions of the waiting times for events that occur both before and after this fixed time are derived. This provides a fairly complete probabilistic analysis of the Inspection Paradox.

Inspection Paradox, Interarrival Time, Poisson Process, Renewal Process, Waiting Time

Marengo, J. , Himes, A. , Reinberger, W. and Farnsworth, D. (2023) Probability Distributions Arising in Connection with the Inspection Paradox for the Poisson Process. Open Journal of Statistics, 13, 16-24. doi: 10.4236/ojs.2023.131002.