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Scan statistics for monitoring data modeled by a negative binomial distribution

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  • Jie Chen
  • Joseph Glaz

Abstract

In this article we investigate the performance of approximations and inequalities for the distribution of scan statistics for independent and identically distributed observations from a geometric and negative binomial distributions. The use of scan statistics are discussed for prospective and retrospective type experiments. These scan statistics can be also used in a sequential type experiments for monitoring data, modeled by a geometric or a negative binomial distribution, for detecting a local change in the waiting time for a specified event or batch of events, respectively. Potential applications include: business, criminology, ecology, entomology, quality control and sampling schemes. Extensions to multiple window scan statistics are discussed as well. Numerical results are presented to evaluate the performance of the approximations and inequalities discussed in this article. A simulation study is included to evaluate the performance of the multiple scan statistics.

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  • Jie Chen & Joseph Glaz, 2016. "Scan statistics for monitoring data modeled by a negative binomial distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(6), pages 1632-1642, March.
    • Handle: RePEc:taf:lstaxx:v:45:y:2016:i:6:p:1632-1642
    DOI: 10.1080/03610926.2014.923460
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    Cited by:

    1. Jie Chen & Thomas Ferguson & Paul Jorgensen, 2020. "Using Scan Statistics for Cluster Detection: Recognizing Real Bandwagons," Methodology and Computing in Applied Probability, Springer, vol. 22(4), pages 1481-1491, December.
    2. Alexandru Amarioarei & Cristian Preda, 2020. "One Dimensional Discrete Scan Statistics for Dependent Models and Some Related Problems," Mathematics, MDPI, vol. 8(4), pages 1-11, April.
    3. Sabine Mercier & Grégory Nuel, 2022. "Duality Between the Local Score of One Sequence and Constrained Hidden Markov Model," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1411-1438, September.

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