The log-likelihood function in terms of the fitted mean response.
Parameters: | endog : array-like
mu : array-like
freq_weights : array-like
scale : float
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Returns: | llf : float
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Notes
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 )}