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_i = sign(Y_i-\mu_i) * \sqrt{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:
piecewise_i = 2 * Y_i * \log(Y_i / \mu_i) - (2 / \alpha) * (1 + \alpha * Y_i) * \log((1 + \alpha * Y_i) / (1 + \alpha * \mu_i))