Poisson Distribution Calculator
Calculate poisson distribution using your data.
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What this tool does
Calculate poisson distribution using your data. Poisson models counts of independent events occurring at a constant average rate in a fixed interval.
How to use the Poisson Distribution Calculator
- Enter or select average rate (λ).
- Enter or select events (k).
- Read the calculated result; change any measurement to compare alternatives.
Formula
P(X=k) = e^(−λ) λ^k / k!; cumulative probabilities sum the PMF; mean = variance = λ
- lam
- Average rate (λ)
- kk
- Events (k)
Poisson models counts of independent events occurring at a constant average rate in a fixed interval.
Worked example
For poisson distribution calculator, the following measurements illustrate the exact method: Average rate (λ): 3; Events (k): 2.
Inputs
- Average rate (λ)3
- Events (k)2
Result
- P(X = k) — exactly (%)22.4
- P(X ≤ k) — at most (%)42.32
- P(X > k) (%)57.68
- Mean (= λ)3
- Variance (= λ)3
Results explained
- P(X = k) — exactly (%)
- P(X = k) — exactly (%) from the formula above. Poisson models counts of independent events occurring at a constant average rate in a fixed interval.
- P(X ≤ k) — at most (%)
- P(X ≤ k) — at most (%) from the formula above. Poisson models counts of independent events occurring at a constant average rate in a fixed interval.
- P(X > k) (%)
- P(X > k) (%) from the formula above. Poisson models counts of independent events occurring at a constant average rate in a fixed interval.
- Mean (= λ)
- Mean (= λ) from the formula above. Poisson models counts of independent events occurring at a constant average rate in a fixed interval.
- Variance (= λ)
- Variance (= λ) from the formula above. Poisson models counts of independent events occurring at a constant average rate in a fixed interval.
Frequently asked questions
P(X=k) = e^(−λ) λ^k / k!; cumulative probabilities sum the PMF; mean = variance = λ
Poisson models counts of independent events occurring at a constant average rate in a fixed interval.
Enter numbers only, in the units and format each label describes. Remove missing values rather than substituting zero, unless zero is a real observation.
No. Results describe the numbers you entered. Statistical inference also depends on sampling design, independence, model fit and interpretation; a p-value is not the probability that a hypothesis is true.
No. Every calculation, including the distribution algorithms, runs entirely in your browser.