Skellam Distribution Calculator
Enter the two Poisson means and the value k.
Result
How to use
- Enter your values in the fields above.
- Press Calculate to see your result instantly.
- Use the Share button to copy a link to your result.
About this calculator
The Skellam distribution is the probability distribution of the difference between two independent Poisson random variables, K = X1 − X2. Its probability mass function is P(K=k) = e^(-(μ1+μ2))·(μ1/μ2)^(k/2)·I_k(2√(μ1·μ2)), where I_k is the modified Bessel function of the first kind; its mean is μ1−μ2 and its variance is μ1+μ2.
It's best known for modeling the goal-difference distribution in sports, where each side's score is treated as an independent Poisson process — a standard technique in football (soccer) score-prediction modeling. This calculator is used by sports analytics modelers, statisticians, and researchers comparing the difference between two independent count processes.
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