Poisson distribution

symbols, variables and units

k: non-negative integer number; λ: average number of events within the window, dimensionless.

applicable conditions and boundaries

Poisson process model requires independent increments and constant event rates; overdispersion requires other models.

formula source code

The following is a copyable LaTeX expression.

P(X=k)=\frac{\lambda^k e^{-\lambda}}{k!}

Reference and Extended Learning

is organized according to model definition and assumptions. Please check actual conditions and original literature before engineering, research and clinical use.