Zero Inflated Poisson Calculator
Calculate a Poisson count mixture with an independent structural-zero probability.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Keep the structural-zero mixture separate from ordinary zeros arising in the Poisson component.
P(0)=π+(1−π)e^(−λ); P(k>0)=(1−π)Poisson(k;λ)
Worked example
π=0.3 and λ=2 give P(0)=0.3+0.7e⁻²≈0.394734698 and overall mean 1.4.
Assumptions and input details
Mixture parameters are supplied, not fitted. This is not a zero-truncated or hurdle model; no exposure offsets, covariates or parameter confidence intervals. Counts are nonnegative integers.
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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