TITLE:
Probability Distributions Arising in Connection with the Inspection Paradox for Bernoulli Trials
AUTHORS:
James E. Marengo, Anne Marino Himes, W. Cade Reinberger, David L. Farnsworth
KEYWORDS:
Inspection Paradox, Interarrival Time, Bernoulli Trial, Renewal Process, Waiting Time
JOURNAL NAME:
Open Journal of Statistics,
Vol.13 No.6,
November
14,
2023
ABSTRACT: In renewal theory, the Inspection Paradox refers to the fact that
an interarrival period in a renewal process which contains a fixed inspection
time tends to be longer than one for the corresponding uninspected process. We
focus on the paradox for Bernoulli trials. Probability distributions and
moments for the lengths of the interarrival periods are derived for the
inspected process, and we compare them to those for the uninspected case.