code: def generalized_entropy_index(b, alpha=2):
      r"""Generalized entropy index measures inequality over a population.
  
      .. math::
  
          \mathcal{E}(\alpha) = \begin{cases}
              \frac{1}{n \alpha (\alpha-1)}\sum_{i=1}^n\left[\left(\frac{b_i}{\mu}\right)^\alpha - 1\right],& \alpha \ne 0, 1,\\
              \frac{1}{n}\sum_{i=1}^n\frac{b_{i}}{\mu}\ln\frac{b_{i}}{\mu},& \alpha=1,\\
              -\frac{1}{n}\sum_{i=1}^n\ln\frac{b_{i}}{\mu},& \alpha=0.
          \end{cases}
  
      Args:
          b (array-like): Parameter over which to calculate the entropy index.
          alpha (scalar): Parameter that regulates the weight given to distances
              between values at different parts of the distribution. A value of 0
              is equivalent to the mean log deviation, 1 is the Theil index, and 2
              is half the squared coefficient of variation.
      """
      if alpha == 0:
          return -(np.log(b / b.mean()) / b.mean()).mean()
      elif alpha == 1:
          # moving the b inside the log allows for 0 values
          return (np.log((b / b.mean()) ** b) / b.mean()).mean()
      else:
          return ((b / b.mean()) ** alpha - 1).mean() / (
              alpha * (alpha - 1)
          )
  
imports: from itertools import permutations
  from typing import Union
  import warnings
  import numpy
  import pandas
  from scipy.special import rel_entr
  from sklearn.metrics import make_scorer, recall_score, precision_score
  from sklearn.metrics import multilabel_confusion_matrix
  from sklearn.metrics._classification import _prf_divide, _check_zero_division
  from sklearn.neighbors import NearestNeighbors
  from sklearn.utils import check_X_y
  from aif360.metrics import ot_metric
  from aif360.sklearn.utils import check_inputs, check_groups
  from aif360.detectors.mdss.ScoringFunctions import BerkJones, Bernoulli
  from aif360.detectors.mdss.MDSS import MDSS
label_desc: Use image node_id 29 for calling a global function with example usage: generalized_entropy_index(b, alpha) and returns: unknown, unknown, unknown