Poisson Event Estimator
Compute probabilities for Poisson events: customer arrivals per hour, server incidents per day, rare diseases per year. Includes a staffing recommendation that picks a capacity with low probability of overload.
Setup
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Result
Distribution (k = 0 to λ+3σ)
When to use Poisson
Use Poisson when events occur independently, at a known average rate, in a continuous interval. Good fits: call-center arrivals, traffic accidents per mile, radioactive decays, rare diseases per population. Bad fits: anything where events cluster (rush-hour traffic) — use a non-homogeneous Poisson process instead.
Who uses it
- Operations managers sizing call-center staffing.
- SREs modeling incident rates and alert thresholds.
- Epidemiologists analyzing rare-disease incidence.
Limitations
- Independent-events assumption is violated for clustered events (rush hour, contagious disease).
- Mean equals variance in Poisson. If your data has over-dispersion (variance > mean), use negative binomial instead.