Zero-Inflated Poisson Regression, with an Application to Defects in Manufacturing
Abstract
Zero-inflated Poisson (ZIP) regression is a model for count data with excess zeros. It assumes that with probability p the only possible observation is 0, and with probability 1 – p, a Poisson(λ) random variable is observed. For example, when manufacturing equipment is properly aligned, defects may be nearly impossible. But when it is misaligned, defects may occur according to a Poisson(λ) distribution. Both the probability p of the perfect, zero defect state and the mean number of defects λ in the imperfect state may depend on covariates. Sometimes p and λ are unrelated; other times p is a simple function of λ such as p = l/(1 + λ T ) for an unknown constant T . In either case, ZIP regression models are easy to fit. The maximum likelihood estimates (MLE's) are approximately normal in large samples, and confidence intervals can be constructed by inverting likelihood ratio tests or using the approximate normality of the MLE's. Simulations suggest that the confidence intervals based on likelihood ratio test...
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None of the cited ZIP model contributions has analysed the role of exposure to risk in terms of distance driven.
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From The Use of Telematics Devices to Improve Automobile Insurance Rates (2019) · cites this paper as Lambert, 1992
An appropriate model for count responses in the presence of structural zeros is the zero-inflated Poisson (ZIP) regression.
“An appropriate model for count responses in the presence of structural zeros is the zero-inflated Poisson (ZIP) regression (Lambert 1992; Kowalski and Tu 2007).”
From Intervention to Strengthen Emotional Self-Regulation in Children with Emerging Mental Health Problems: Proximal Impact on School Behavior (2010) · cites this paper as Lambert 1992
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- Authors
- Lambert, D.
- Affiliations
- AT&T (United States) (US)
- Corresponding author
- Lambert, Diane
- Venue
- Technometrics
- Publisher
- JSTOR
- Published
- 1992-02
- Volume
- 34
- Issue
- 1
- Pages
- 1
- ISSN
- 0040-1706 (ISSN-L)
- OpenAlex
- W2119634512
- Cited by
- 3,988
- References
- 1
- Citations by year
- 2026: 189 · 2025: 191 · 2024: 199 · 2023: 190 · 2022: 195 · 2021: 275 · 2020: 220 · 2019: 191 · 2018: 189 · 2017: 179 · 2016: 202 · 2015: 211 · 2014: 193 · 2013: 187 · 2012: 196
- FWCI
- 8.52
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Technometrics (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Distribution Estimation and Applications
- Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
- Keywords
- zero-inflated Poisson regression, excess zeros, count data, manufacturing defects, maximum likelihood estimation
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