statsmodels.discrete.discrete_model.Poisson.score Poisson.score(params) [source] Poisson model score (gradient) vector of the log-likelihood Parameters: params : array-like The parameters of the model Returns: score : ndarray, 1-D The score vector of the model, i.e. the first derivative of the loglikelihood function, evaluated at params Notes where the loglinear model is assumed

statsmodels.genmod.families.family.Poisson.resid_dev Poisson.resid_dev(endog, mu, scale=1.0) [source] Poisson deviance residual Parameters: endog : array-like Endogenous response variable mu : array-like Fitted mean response variable scale : float, optional An optional argument to divide the residuals by scale Returns: resid_dev : array Deviance residuals as defined below Notes resid_dev = sign(endog-mu)*sqrt(2*endog*log(endog/mu)-2*(endog-mu))

statsmodels.genmod.families.family.Poisson.resid_anscombe Poisson.resid_anscombe(endog, mu) [source] Anscombe residuals for the Poisson exponential family distribution Parameters: endog : array-like Endogenous response variable mu : array-like Fitted mean response variable Returns: resid_anscombe : array The Anscome residuals for the Poisson family defined below Notes resid_anscombe is defined

statsmodels.genmod.families.family.Poisson.predict Poisson.predict(mu) Linear predictors based on given mu values. Parameters: mu : array The mean response variables Returns: lin_pred : array Linear predictors based on the mean response variables. The value of the link function at the given mu.

statsmodels.discrete.discrete_model.Poisson.predict Poisson.predict(params, exog=None, exposure=None, offset=None, linear=False) Predict response variable of a count model given exogenous variables. Notes If exposure is specified, then it will be logged by the method. The user does not need to log it first.

statsmodels.discrete.discrete_model.Poisson.pdf Poisson.pdf(X) [source] Poisson model probability mass function Parameters: X : array-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. Notes The PMF is defined as where assumes the loglinear model. I.e., The parameter X is in the above formula.

statsmodels.discrete.discrete_model.Poisson.loglikeobs Poisson.loglikeobs(params) [source] Loglikelihood for observations of Poisson model Parameters: params : array-like The parameters of the model. Returns: loglike : ndarray (nobs,) The log likelihood for each observation of the model evaluated at params. See Notes Notes for observations

statsmodels.genmod.families.family.Poisson.loglike Poisson.loglike(endog, mu, scale=1.0) [source] Loglikelihood function for Poisson exponential family distribution. Parameters: endog : array-like Endogenous response variable mu : array-like Fitted mean response variable scale : float, optional The default is 1. Returns: llf : float The value of the loglikelihood function evaluated at (endog,mu,scale) as defined below. Notes llf = scale * sum(-mu + endog*log(mu) - gammaln(endog+1

statsmodels.discrete.discrete_model.Poisson.loglike Poisson.loglike(params) [source] Loglikelihood of Poisson model Parameters: params : array-like The parameters of the model. Returns: loglike : float The log-likelihood function of the model evaluated at params. See notes. Notes

statsmodels.discrete.discrete_model.Poisson.jac Poisson.jac(*args, **kwds) jac is deprecated, use score_obs instead! Use score_obs method. jac will be removed in 0.7 Poisson model Jacobian of the log-likelihood for each observation Parameters: params : array-like The parameters of the model Returns: score : ndarray (nobs, k_vars) The score vector of the model evaluated at params Notes for observations where the loglinear model is assumed