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Estimating the Change Point of Correlated Poisson Count Processes

Summary: [This abstract is based on the authors' abstract.] Knowing the time of change would narrow the search to find and identify the variables disturbing a process. The knowledge of the change point can greatly aid practitioners in detecting and removing the special cause(s). Count processes with an autocorrelation structure are commonly observed in real-world applications and can often be modeled by the first-order integer-valued autoregressive (INAR) model. The most widely used marginal distribution for count processes is Poisson. In this study, change-point estimators are proposed for the parameters of correlated Poisson count processes. To do this, Newton’s method is first used to approximate the parameters of the process. Then, maximum likelihood estimators of the process change point are developed. The performances of these estimators are next evaluated when they are employed in a combined exponentially weighted moving average (EWMA) and c scheme. Finally, for the rate parameter, the proposed estimator is compared with the estimator developed for independent observations.

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  • Topics: Process Management
  • Keywords: Count estimation, Poisson distribution, Maximum likelihood estimate (MLE), Autocorrelation, Exponentially weighted moving average (EWMA), First order autoregressive models, Multivariate time series, Shift point
  • Author: Torkamani, Elnaz Asghari; Niaki, Seyed Taghi Akhavan; Aminnayeri, Majid ; Davoodi, Mehdi;
  • Journal: Quality Engineering