statsmodels.genmod.families.family.InverseGaussian.loglike_obs

InverseGaussian.loglike_obs(endog, mu, var_weights=1.0, scale=1.0)

The log-likelihood function for each observation in terms of the fitted mean response for the Inverse Gaussian distribution.

Parameters:

• endog (array) – Usually the endogenous response variable.
• mu (array) – Usually but not always the fitted mean response variable.
• var_weights (array-like) – 1d array of variance (analytic) weights. The default is 1.
• scale (float) – The scale parameter. The default is 1.

Returns:

ll_i – The value of the loglikelihood evaluated at (endog, mu, var_weights, scale) as defined below.

Return type:

float

Notes

$$ll_i = -1/2 * (var\_weights_i * (endog_i - \mu_i)^2 / (scale * endog_i * \mu_i^2) + \ln(scale * \endog_i^3 / var\_weights_i) - \ln(2 * \pi))$$