A user implemented a Gini coefficient in Python

def gini(x):

    # Mean absolute difference.

    mad = np.abs(np.subtract.outer(x, x)).mean()

    # Relative mean absolute difference

    rmad = mad / np.mean(x)

    # Gini coefficient is half the relative mean absolute difference.

    return 0.5 * rmad

How is it possible to adjust to take an array of weights as a second vector?

For example

gini([1, 2, 3]) # No weight: 0.22.

gini([1, 1, 1, 2, 2, 3]) # Manually weighted: 0.23.

gini([1, 2, 3], weight=[3, 2, 1]) # Should also give 0.23.

In such case the calculation of mad need to be replaced by the following code

x = np.array([1, 2, 3, 6])

c = np.array([2, 3, 1, 2])

count = np.multiply.outer(c, c)

mad = np.abs(np.subtract.outer(x, x) * count).sum() / count.sum()

np.mean(x)can be replaced by

np.average(x, weights=c)

Below is the full function

def gini(x, weights=None):

    if weights is None:

        weights = np.ones_like(x)

    count = np.multiply.outer(weights, weights)

    mad = np.abs(np.subtract.outer(x, x) * count).sum() / count.sum()

    rmad = mad / np.average(x, weights=weights)

    return 0.5 * rmad

For checking the result, gini2() uses Numpy.repeat() to repeat elements

def gini2(x, weights=None):

    if weights is None:

        weights = np.ones(x.shape[0], dtype=int)

    x = np.repeat(x, weights)

    mad = np.abs(np.subtract.outer(x, x)).mean()

    rmad = mad / np.mean(x)

    return 0.5 * rmad