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

$$l{l}_i=-1/2\ast (var\mathrm{\_}weight{s}_i\ast (endo{g}_i-{\mu }_i{)}^2/(scale\ast endo{g}_i\ast {\mu }_i^2)+\ln (scale\ast {\text{endog}}_i^3/var\mathrm{\_}weight{s}_i)-\ln (2\ast \pi ))$$