%0 Journal Article
%T Probability Distributions Arising in Connection with the Inspection Paradox for the Poisson Process
%A James E. Marengo
%A Anne Marino Himes
%A W. Cade Reinberger
%A David L. Farnsworth
%J Open Journal of Statistics
%P 16-24
%@ 2161-7198
%D 2023
%I Scientific Research Publishing
%R 10.4236/ojs.2023.131002
%X 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
dist</span><span style=\"font-family:Verdana;\">ributions and moments of the lengths of
the interarrival periods other than the one containing this fixed time for the
case of the time-homogeneous</span><span style=\"font-family:Verdana;\"> 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.
%K Inspection Paradox
%K Interarrival Time
%K Poisson Process
%K Renewal Process
%K Waiting Time
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=123151