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Probability Distributions Arising In Connection With The Inspection Paradox For Bernoulli Trials., James E. Marengo, Anne Marino Himes, W. Cade Reinberger, David L. Farnsworth
Probability Distributions Arising In Connection With The Inspection Paradox For Bernoulli Trials., James E. Marengo, Anne Marino Himes, W. Cade Reinberger, David L. Farnsworth
Articles
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.
Probability Distributions Arising In Connection With The Inspection Paradox For The Poisson Process, James E. Marengo, Anne Marino Himes, David L. Farnsworth, W. Cade Reinberger
Probability Distributions Arising In Connection With The Inspection Paradox For The Poisson Process, James E. Marengo, Anne Marino Himes, David L. Farnsworth, W. Cade Reinberger
Articles
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 …