NegativeBinomial.loglike()

statsmodels.genmod.families.family.NegativeBinomial.loglike

NegativeBinomial.loglike(endog, mu, freq_weights=1.0, scale=1.0) [source]

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

Parameters:

Parameters:	endog : array-like Endogenous response variable mu : array-like The fitted mean response values freq_weights : array-like 1d array of frequency weights. The default is 1. scale : float The scale parameter. The default is 1.
Returns:	llf : float The value of the loglikelihood function evaluated at (endog,mu,freq_weights,scale) as defined below.

endog : array-like

Endogenous response variable

mu : array-like

The fitted mean response values

freq_weights : array-like

1d array of frequency weights. The default is 1.

scale : float

The scale parameter. The default is 1.

Returns:

llf : float

The value of the loglikelihood function evaluated at (endog,mu,freq_weights,scale) as defined below.

Defined as:

$llf = \sum_i freq\_weights_i * (Y_i * \log{(\alpha * e^{\eta_i} / (1 + \alpha * e^{\eta_i}))} - \log{(1 + \alpha * e^{\eta_i})}/ \alpha + Constant)$

where $Constant$ is defined as:

$Constant = \ln \Gamma{(Y_i + 1/ \alpha )} - \ln \Gamma(Y_i + 1) - \ln \Gamma{(1/ \alpha )}$

© 2009–2012 Statsmodels Developers
© 2006–2008 Scipy Developers
© 2006 Jonathan E. Taylor
Licensed under the 3-clause BSD License.
http://www.statsmodels.org/stable/generated/statsmodels.genmod.families.family.NegativeBinomial.loglike.html