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Poisson distribution calculator

The Poisson distribution calculator returns exact probabilities and quantiles for a count with mean λ.

What is Poisson distribution calculator?

The Poisson models counts of independent events in a fixed exposure — the distribution behind incidence rates, particle counts and defect counts, and the limit of a binomial when n is large and p small.

As with the binomial the support is discrete, so all four tail forms are reported rather than inferred from one another.

When should I use Poisson distribution calculator?

Finding the probability of k or more events at a known rate.
Checking an exact Poisson p-value.
Setting a count threshold for a monitoring rule.

What data does it need?

Distribution parameters, plus a value x, a tail probability p, or both.

What does it report?

For x: the density or exact probability and each tail. For p: the lower, upper and two-tailed critical values.

What does it assume?

None — this evaluates a distribution rather than testing data against one.