class statsmodels.discrete.discrete_model.Poisson(endog, exog, offset=None, exposure=None, missing='none', **kwargs)[source]

Poisson model for count data

  • endog (array-like) – 1-d endogenous response variable. The dependent variable.
  • exog (array-like) – A nobs x k array where nobs is the number of observations and k is the number of regressors. An intercept is not included by default and should be added by the user. See
  • offset (array_like) – Offset is added to the linear prediction with coefficient equal to 1.
  • exposure (array_like) – Log(exposure) is added to the linear prediction with coefficient equal to 1.
  • missing (str) – Available options are ‘none’, ‘drop’, and ‘raise’. If ‘none’, no nan checking is done. If ‘drop’, any observations with nans are dropped. If ‘raise’, an error is raised. Default is ‘none.’

A reference to the endogenous response variable


A reference to the exogenous design.



cdf(X) Poisson model cumulative distribution function
cov_params_func_l1(likelihood_model, xopt, …) Computes cov_params on a reduced parameter space corresponding to the nonzero parameters resulting from the l1 regularized fit.
fit([start_params, method, maxiter, …]) Fit the model using maximum likelihood.
fit_constrained(constraints[, start_params]) fit the model subject to linear equality constraints
fit_regularized([start_params, method, …]) Fit the model using a regularized maximum likelihood.
from_formula(formula, data[, subset, drop_cols]) Create a Model from a formula and dataframe.
hessian(params) Poisson model Hessian matrix of the loglikelihood
hessian_factor(params) Poisson model Hessian factor
information(params) Fisher information matrix of model
initialize() Initialize is called by statsmodels.model.LikelihoodModel.__init__ and should contain any preprocessing that needs to be done for a model.
loglike(params) Loglikelihood of Poisson model
loglikeobs(params) Loglikelihood for observations of Poisson model
pdf(X) Poisson model probability mass function
predict(params[, exog, exposure, offset, linear]) Predict response variable of a count model given exogenous variables.
score(params) Poisson model score (gradient) vector of the log-likelihood
score_factor(params) Poisson model score_factor for each observation
score_obs(params) Poisson model Jacobian of the log-likelihood for each observation


endog_names Names of endogenous variables
exog_names Names of exogenous variables