Binomial exponential family distribution.

linka link instance, optional

The default link for the Binomial family is the logit link. Available links are logit, probit, cauchy, log, and cloglog. See statsmodels.genmod.families.links for more information.


endog for Binomial can be specified in one of three ways: A 1d array of 0 or 1 values, indicating failure or success respectively. A 2d array, with two columns. The first column represents the success count and the second column represents the failure count. A 1d array of proportions, indicating the proportion of successes, with parameter var_weights containing the number of trials for each row.

Binomial.linka link instance

The link function of the Binomial instance

Binomial.variancevarfunc instance

variance is an instance of statsmodels.genmod.families.varfuncs.binary


deviance(endog, mu[, var_weights, …])

The deviance function evaluated at (endog, mu, var_weights, freq_weights, scale) for the distribution.


Fitted values based on linear predictors lin_pred.

initialize(endog, freq_weights)

Initialize the response variable.

loglike(endog, mu[, var_weights, …])

The log-likelihood function in terms of the fitted mean response.

loglike_obs(endog, mu[, var_weights, scale])

The log-likelihood function for each observation in terms of the fitted mean response for the Binomial distribution.


Linear predictors based on given mu values.

resid_anscombe(endog, mu[, var_weights, scale])

The Anscombe residuals

resid_dev(endog, mu[, var_weights, scale])

The deviance residuals


The starting values for the IRLS algorithm for the Binomial family.



Weights for IRLS steps