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

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

Returns the value of the deviance function.

Parameters :

Y : array-like

Endogenous response variable

mu : array-like

Fitted mean response variable

scale : float, optional

An optional scale argument

Returns :

deviance : float

Deviance function as defined below

Notes

deviance = sum(piecewise)

where piecewise is defined as

if $Y_{i} == 0:$

piecewise_i = $2\log\left(1+\alpha*\mu\right)/\alpha$

if $Y_{i} > 0$ :

piecewise_i = $2 Y \log(Y/\mu)-2/\alpha(1+\alpha Y)*\log((1+\alpha Y)/(1+\alpha\mu))$