statsmodels.genmod.families.family.Tweedie.deviance¶

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

$D = \sum{2 * freq\_weights * resid\_dev_i}$