Zero-Inflated Poisson Distribution
K ~ ZIP(π, λ)
Excess-Zeros / Mixture Family • Published August 11, 2026
Diane Lambert's 1992 fix for count data with more zeros than the Poisson predicts: history from manufacturing defect-count modeling, a two-component mixture of a 'structural' zero and an ordinary already-published Poisson process, a contrast with the already-published Negative Binomial's different (rate-heterogeneity) explanation for the same symptom of overdispersion, a maximum-likelihood system with no closed form verified against an independent statsmodels fit, and simulation via the mixture's own defining construction.
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About This Reference Sheet
Diane Lambert's 1992 fix for count data with more zeros than the Poisson predicts: history from manufacturing defect-count modeling, a two-component mixture of a 'structural' zero and an ordinary already-published Poisson process, a contrast with the already-published Negative Binomial's different (rate-heterogeneity) explanation for the same symptom of overdispersion, a maximum-likelihood system with no closed form verified against an independent statsmodels fit, and simulation via the mixture's own defining construction.
Support
k ∈ {0, 1, 2, ...}
Parameters
π ∈ [0,1) (structural-zero probability), λ > 0 (Poisson mean)