Negative Binomial Deviance Residual
Parameters: | endog : array-like
mu : array-like
scale : float, optional
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Returns: | resid_dev : array
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Notes
resid_dev = sign(endog-mu) * sqrt(piecewise)
where piecewise is defined as
If Y_i = 0:
piecewise_i = 2*log(1+alpha*mu)/alpha
If Y_i > 0:
piecewise_i = 2*Y*log(Y/\mu) - 2/\alpha * (1 + \alpha * Y) * \log((1 + \alpha * Y)/(1 + \alpha * \mu))