statsmodels.genmod.families.family.NegativeBinomial.deviance¶

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

Returns the value of the deviance function.

Parameters:

endog : array-like

Endogenous response variable

mu : array-like

Fitted mean response variable

freq_weights : array-like

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

scale : float, optional

An optional scale argument. The default is 1.

Returns:

deviance : float

Deviance function as defined below

Notes

$D = \sum_i piecewise_i$ where $piecewise_i$ is defined as:

If $Y_{i} = 0$ :

$piecewise_i = 2* \log(1 + \alpha * \mu_i) / \alpha$

If $Y_{i} > 0$ :