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Rewrite Gini coefficient in O(n log n) #937

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17 changes: 9 additions & 8 deletions quantecon/_inequality.py
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Original file line number Diff line number Diff line change
Expand Up @@ -4,7 +4,7 @@
"""

import numpy as np
from numba import njit, prange
from numba import njit


@njit
Expand Down Expand Up @@ -54,7 +54,7 @@ def lorenz_curve(y):
return cum_people, cum_income


@njit(parallel=True)
@njit
def gini_coefficient(y):
r"""
Implements the Gini inequality index
Expand All @@ -76,11 +76,13 @@ def gini_coefficient(y):
https://en.wikipedia.org/wiki/Gini_coefficient
"""
n = len(y)
i_sum = np.zeros(n)
for i in prange(n):
for j in range(n):
i_sum[i] += abs(y[i] - y[j])
return np.sum(i_sum) / (2 * n * np.sum(y))
y_s = np.sort(y)
i_weighted = 0.0
total = 0.0
for i in range(n):
i_weighted += (i + 1) * y_s[i]
total += y_s[i]
return (2 * i_weighted) / (n * total) - (n + 1) / n


def shorrocks_index(A):
Expand Down Expand Up @@ -152,4 +154,3 @@ def rank_size(data, c=1.0):
rank_data = np.arange(len(w)) + 1
size_data = w
return rank_data, size_data

6 changes: 5 additions & 1 deletion quantecon/tests/test_inequality.py
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Original file line number Diff line number Diff line change
Expand Up @@ -59,6 +59,11 @@ def test_gini_coeff():
coeff = gini_coefficient(y)
assert_allclose(expected, coeff, rtol=1e-01)

# Regression against the pairwise definition
y = np.array([1.0, 2.0, 4.0, 8.0])
expected = np.abs(y[:, None] - y).sum() / (2 * len(y) * y.sum())
assert_allclose(expected, gini_coefficient(y))

# Tests Weibull: G = 1 - 2**(-1/a)
a = np.random.randint(2, 15)
expected = 1 - 2 ** (-1 / a)
Expand Down Expand Up @@ -130,4 +135,3 @@ def test_rank_size():
r_sqval_exp = r_value_exp**2

assert_raises(AssertionError, assert_allclose, r_sqval_exp, 1, rtol=1e-3)