class statsmodels.discrete.discrete_model.NegativeBinomial(endog, exog, loglike_method='nb2', offset=None, exposure=None, missing='none', **kwargs)[source]

Negative Binomial 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

loglike_method : string

Log-likelihood type. ‘nb2’,’nb1’, or ‘geometric’. Fitted value \mu Heterogeneity parameter \alpha

  • nb2: Variance equal to \mu + \alpha\mu^2 (most common)
  • nb1: Variance equal to \mu + \alpha\mu
  • geometric: Variance equal to \mu + \mu^2

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.’



Greene, W. 2008. “Functional forms for the negtive binomial model
for count data”. Economics Letters. Volume 99, Number 3, pp.585-590.
Hilbe, J.M. 2011. “Negative binomial regression”. Cambridge University


endog (array) A reference to the endogenous response variable
exog (array) A reference to the exogenous design.


cdf(X) The cumulative distribution function of the model.
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_regularized([start_params, method, ...])
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 for negative binomial model
pdf(X) The probability density (mass) function of the model.
predict(params[, exog, exposure, offset, linear]) Predict response variable of a count model given exogenous variables.