statsmodels.genmod.families.family.InverseGaussian.loglike_obs¶

InverseGaussian.loglike_obs(endog, mu, var_weights=1.0, scale=1.0)[source]¶

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

Parameters:¶

endogndarray

Usually the endogenous response variable.

mundarray

Usually but not always the fitted mean response variable.

var_weightsarray_like

1d array of variance (analytic) weights. The default is 1.

scalefloat

The scale parameter. The default is 1.

Returns:¶

ll_ifloat

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

Notes

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