# statsmodels.discrete.discrete_model.Poisson.pdf¶

Poisson.pdf(X)[source]

Poisson model probability mass function

Parameters: X (array-like) – X is the linear predictor of the model. See notes. pdf – The value of the Poisson probability mass function, PMF, for each point of X. ndarray

Notes

The PMF is defined as

$\frac{e^{-\lambda_{i}}\lambda_{i}^{y_{i}}}{y_{i}!}$

where $$\lambda$$ assumes the loglinear model. I.e.,

$\ln\lambda_{i}=x_{i}\beta$

The parameter X is $$x_{i}\beta$$ in the above formula.