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Updated 2026-03-07 UTC
Poisson Distribution Calculator — PMF and CDF
Compute Poisson probabilities for count data with GetCalcMaster’s stats functions. Includes worked examples (educational).
The Poisson distribution models event counts over a fixed interval when events occur independently at a constant average rate λ. Use this guide to compute PMF and CDF values.
Important: This content and tool are for educational purposes only. Outputs are estimates; always cross‑verify with official sources and/or a qualified professional.
What this calculator is
The Statistics Calculator is an interactive tool inside GetCalcMaster. It’s designed to help you explore scenarios, understand formulas, and document assumptions.
Key features
- Immediate results as you change inputs
- Transparent assumptions and explainable outputs
- Works well with the built‑in Notebook for saving scenarios
Formula
PMF: P(X=k) = e^(−λ) λ^k / k!
CDF: P(X ≤ k)Quick examples
poissonpmf(5, 3.2) # ≈ 0.113979poissoncdf(5, 3.2) # ≈ 0.894592# CDF monotonic check poissoncdf(6, 3.2) - poissoncdf(5, 3.2)
Verification tips
- λ must be positive and represents the expected count in your chosen interval.
- CDF should be non-decreasing as k increases.
- If your rate changes over time or events aren’t independent, the Poisson model may not fit.
Common mistakes
- Using a negative λ (not valid).
- Confusing λ (expected count per interval) with a probability p.
- Forgetting to match λ to the same interval length you’re modeling.
How to use it (quick steps)
- Choose λ (average rate) and k (event count).
- Open the Statistics Calculator.
- Use poissonpmf(k, λ) for exact probabilities and poissoncdf(k, λ) for cumulative probabilities.
- Sanity check: probabilities must be between 0 and 1; CDF increases with k.
- Record interval definition and whether constant-rate assumptions are reasonable.
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Pearson r interpretation cautions.
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FAQ
What does poissonpmf(k,λ) compute?
The probability of observing exactly k events when the expected count is λ.
What does poissoncdf(k,λ) compute?
The probability of observing at most k events: P(X ≤ k).
When is Poisson a good model?
When events are independent and occur at a roughly constant average rate over a fixed interval.
Tip: For reproducible work, save your inputs and reasoning in Notebook.