Recently, there was a discussion about this in #28144 (PR #28156).

Quote from one of the core developers (#28144 (comment)):

You will find this simple formula implemented in some of our examples, too. Because it is so simple, I‘m against adding it to the already large metrics API.

I'm not sure, but there seems to be 2 different gini index/coefficient definitions:

1. Defined on the output of a binary classifier:
   Defines here: https://en.wikipedia.org/wiki/Gini_coefficient#Relation_to_other_statistical_measures and in roc_auc_score() notes (gini = 2 * roc_auc - 1)

2. Defined on a more general float variable. (not necessarily the output of a binary classifier):
   Defines here: https://en.wikipedia.org/wiki/Gini_coefficient and in this code example:

   ordered_samples, cum_claims = lorenz_curve(y_true, y_pred, exposure)
   gini = 1 - 2 * auc(ordered_samples, cum_claims)

   Note that this code does not use roc_auc_score(), it uses lorenz_curve() and then calculate the area under the Lorenz curve (not the area under the ROC curve) using auc()

You are right, but I'm assuming that a similar argument (too simple to include in the library) could be made for Gini coefficient you are requesting (sklearn/core-devs will know better).

See #21320 (comment) .

Almost a duplicate: #10003.