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 statsmodels.tools.add_constant.
  • 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.’

array – A reference to the endogenous response variable


array – A reference to the exogenous design.



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


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 the model using maximum likelihood.
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) The Hessian matrix of the model
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 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.
score(params) Score vector of model.


endog_names Names of endogenous variables
exog_names Names of exogenous variables

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© 2006 Jonathan E. Taylor
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