statsmodels.genmod.families.family.Tweedie.deviance¶
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Tweedie.
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
When \(p = 1\),
\[resid\_dev_i = \mu\]when \(endog = 0\) and
\[resid\_dev_i = endog * \log(endog / \mu) + (\mu - endog)\]otherwise.
When \(p = 2\),
\[resid\_dev_i = (endog - \mu) / \mu - \log(endog / \mu)\]For all other p,
\[resid\_dev_i = endog ^{2 - p} / ((1 - p) * (2 - p)) - endog * \mu ^{1 - p} / (1 - p) + \mu ^{2 - p} / (2 - p)\]Once \(resid\_dev_i\) is calculated, then calculate deviance as
\[D = \sum{2 * freq\_weights * resid\_dev_i}\]