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.

Returns:

pdf : ndarray

The value of the Poisson probability mass function, PMF, for each point of X.

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.