Zero Inflated Poisson
Separate structural zeros from ordinary Poisson zeros and see how mixing changes count variability.
Free theory articleSeparate structural zeros from ordinary Poisson zeros and see how mixing changes count variability.
Concept & interpretation
Many real-world counts exhibit more zeros than a standard Poisson distribution predicts. A zero-inflated Poisson (ZIP) model mixes a structural point mass at 0 with weight π and a regular Poisson(λ) distribution with weight 1 - π. This allows for separating zeros from the structural state from zeros arising by chance in the active Poisson state. An observed zero alone does not identify its latent source; the stacked bar is a model decomposition.
Interactive Experiment
Open the Zero Inflated Poisson explorer.
- Set Poisson rate lambda to 2 and Structural-zero probability to 0.25.
- Select Count k = 2. Notice the calculated PMF is approximately 0.203002924855.
- Change the count to 0. The Total P(K=0) displays 0.351501462427. The bar chart at 0 stacks the structural zero part (0.25) and the Poisson zero part (~0.1015).
- Adjust the structural-zero probability to 0. Notice the variance drops to equal the mean, recovering a standard Poisson distribution.