statsmodels.discrete.discrete_model.Poisson.pdf¶

Poisson.pdf(X)[source]¶

Poisson model probability mass function

Parameters:¶

Xarray_like

X is the linear predictor of the model. See notes.

Returns:¶

pdfndarray

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.