Distributions
  1. Home
  3. Distributions
  5. Poisson Distribution

Poisson Distribution

Discrete probability of a given number of events occurring in a fixed interval.

Probability Mass FunctionPMF = P(X = x)
Cumulative Distribution FunctionCDF = F(x)
Probability in an Interval
Compute the probability that X falls between two values. For discrete distributions, this is the sum of probabilities P(X = k) for all integers k from a to b.
P(a ≤ X ≤ b)
Quantiles (Inverse CDF)
Pick a probability p and read the corresponding quantile xₚ where F(xₚ) = p.
Quantile xₚ (where F(xₚ) = p)
In Poisson Distribution, selected probability p: 0.9500 (95.00%)

Parameters

Adjust the parameters and (optionally) add up to 3 curves to compare different settings side‑by‑side.

0 curves shown

Estimating parameters from data

If you’re fitting this distribution to observed data, these are common plug‑in estimates you can start with.

Rate (λ)

Calculate the average number of events per unit time/space from your data.