statsmodels.discrete.discrete_model.Poisson.pdf¶
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Poisson.pdf(X)[source]¶ Poisson model probability mass function
- Parameters
- Xarray_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.
- pdf
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.