stats

Poisson Distribution

P(X=k), cumulative CDF, tail probabilities, and PMF bar chart for any λ — with range mode and real-world presets.

Presets

Parameters

Rate λ (avg events per period)

Time period t (optional, scales λ)

Evaluation Mode

Events to evaluate k

Results

Effective λ—

P(X = k)—

P(X ≤ k) — CDF—

P(X > k)—

P(X ≥ k)—

Mean = λ—

Variance = λ—

Std Dev = √λ—

P(X=k) = e^(k·ln λ − λ − ln k!) · log-sum avoids overflow

ln(k!) via lgamma (Lanczos, g=7)
Normal approximation used when λ > 100