Change-Point Methods for Overdispersed Count Data Brian A. Wilken

ISBN: 9781249592365

Published: October 9th 2012

Paperback

114 pages


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Change-Point Methods for Overdispersed Count Data  by  Brian A. Wilken

Change-Point Methods for Overdispersed Count Data by Brian A. Wilken
October 9th 2012 | Paperback | PDF, EPUB, FB2, DjVu, talking book, mp3, ZIP | 114 pages | ISBN: 9781249592365 | 4.16 Mb

A control chart is often used to detect a change in a process. Following a control chart signal, knowledge of the time and magnitude of the change would simplify the searchforand identification of the assignable cause. In this research, emphasis isMoreA control chart is often used to detect a change in a process. Following a control chart signal, knowledge of the time and magnitude of the change would simplify the searchforand identification of the assignable cause. In this research, emphasis is placed on count processes where overdispersion has occurred.

Overdispersion is common in practice and occurs when the observed variance is larger than the theoretical variance of the assumed model. Although the Poisson model is often used to model count data, the two parameter gamma-Poisson mixture parameterization of the negative binomial distribution is often a more adequate model for overdispersed count data.

In this research effort, maximum likelihood estimators for the time of a step change in each of the parameters of the gamma-Poisson mixture model are derived. MonteCarlo simulation is used to evaluate the rootmean square error performance of these estimators to determine their utility in estimating the change point, following a control chart signal. Results show that the estimators provide process engineers with accurate and useful estimates for the time of step change.

In addition, an approach for estimating a confidence set for the process change point will be presented.



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