Quick guide
How to use this calculator
- Enter the observations, probabilities, model parameters, or summary statistics requested by the visible labels.
- Keep every value on the same scale and confirm that the selected sampling relationship, distribution, and tail convention match the question you are investigating.
- Read the result together with its assumptions and interpretation. Statistical output summarizes uncertainty under a model; it does not repair biased data or establish causation.
Calculation method
How the skellam distribution calculator works
If X~Poisson(λ₁) and Y~Poisson(λ₂) independently, D=X−Y follows a Skellam distribution.
The sign identifies which count is larger; the mean difference is λ₁−λ₂ and variance is λ₁+λ₂.
Worked example
Skellam Distribution example
For equal means λ₁=λ₂=1, P(D=0)=e⁻²I₀(2)≈0.308508.
If X~Poisson(λ₁) and Y~Poisson(λ₂) independently, D=X−Y follows a Skellam distribution.
Supported inputs
Precision and limits
Model and design
The two counts must be independent Poisson variables measured over comparable exposure; the calculator reports point mass rather than a cumulative tail.
Numerical scope
Inputs use double-precision numerical methods with guarded domains. Datasets accept up to 10,000 finite plain-decimal values. Extremely large parameters or probabilities deep in a numerical tail may require specialist statistical software.
Interpretation
The sign identifies which count is larger; the mean difference is λ₁−λ₂ and variance is λ₁+λ₂.
Decision boundary
The calculator does not validate how data were collected, diagnose dependence or bias, choose a scientifically meaningful effect, or replace review by a qualified statistician for consequential research, medical, regulatory, safety, or policy decisions.
Privacy
Entered values and calculated results stay in this browser and are not sent to an analytics service.
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