Sojourning With the Homogeneous Poisson Process
Piaomu Liu and
Edsel A. Peña
The American Statistician, 2016, vol. 70, issue 4, 413-423
Abstract:
In this pedagogical article, distributional properties, some surprising, pertaining to the homogeneous Poisson process (HPP), when observed over a possibly random window, are presented. Properties of the gap-time that covered the termination time and the correlations among gap-times of the observed events are obtained. Inference procedures, such as estimation and model validation, based on event occurrence data over the observation window, are also presented. We envision that through the results in this article, a better appreciation of the subtleties involved in the modeling and analysis of recurrent events data will ensue, since the HPP is arguably one of the simplest among recurrent event models. In addition, the use of the theorem of total probability, Bayes’ theorem, the iterated rules of expectation, variance and covariance, and the renewal equation could be illustrative when teaching distribution theory, mathematical statistics, and stochastic processes at both the undergraduate and graduate levels. This article is targeted toward both instructors and students.
Date: 2016
References: View complete reference list from CitEc
Citations:
Downloads: (external link)
http://hdl.handle.net/10.1080/00031305.2016.1200484 (text/html)
Access to full text is restricted to subscribers.
Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text
Persistent link: https://EconPapers.repec.org/RePEc:taf:amstat:v:70:y:2016:i:4:p:413-423
Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/UTAS20
DOI: 10.1080/00031305.2016.1200484
Access Statistics for this article
The American Statistician is currently edited by Eric Sampson
More articles in The American Statistician from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().