Scan statistics for monitoring data modeled by a negative binomial distribution

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.

Cite this work

No public copy is stored for this record, so only the metadata is cited.

Stored only when both papers are in the corpus — 12 citations exist upstream.

Papers that cite the same references — the relational fallback while embeddings are still backfilling.