gini.py

import numpy as np
import random

import plotly
import plotly.graph_objs as go


N_QUINTILES = 5

def gini(array):
    """Calculate the Gini coefficient of a numpy array.
    Copied from https://github.com/oliviaguest/gini .
    """
    array = np.asarray(array)

    # based on bottom eq:
    # http://www.statsdirect.com/help/generatedimages/equations/equation154.svg
    # from:
    # http://www.statsdirect.com/help/default.htm#nonparametric_methods/gini.htm
    # All values are treated equally, arrays must be 1d:
    array = array.flatten()
    array = np.sort(array)
    index = np.arange(1,array.shape[0]+1)
    n = array.shape[0]
    return ((np.sum((2 * index - n  - 1) * array)) / float(n * np.sum(array)))

def transfer(orig_data, gini_diff, from_quintile, to_quintiles):
    total_wealth = np.sum(orig_data)

    gini_diff_per_amount_transfered = 0
    for to_q in to_quintiles:
        transfer_distance = float(abs(to_q - from_quintile)) / N_QUINTILES
        gini_diff_per_amount_transfered += transfer_distance * 2 / float(total_wealth)

    amount_to_transfer = gini_diff / gini_diff_per_amount_transfered

    new_data = np.copy(orig_data)
    for to_q in to_quintiles:
        new_data[to_q] = new_data[to_q] + amount_to_transfer
    new_data[from_quintile] = new_data[from_quintile] - len(to_quintiles) * amount_to_transfer

    return new_data

def poorest_give_to_richest(orig_data, gini_diff):
    return transfer(orig_data, gini_diff, 0, [4])

def poorest_give_to_everyone_equally(orig_data, gini_diff):
    return transfer(orig_data, gini_diff, 0, [1,2,3,4])

def everyone_gives_to_rich_equally(orig_data, gini_diff):
    return transfer(orig_data, -gini_diff, 4, [0,1,2,3])

def random_income_distribution(total_wealth=10000):
    weights = [random.random() for _ in range(0, N_QUINTILES)]
    return [int(total_wealth * w / sum(weights)) for w in weights].sort()

def graph(old_data, transfer_fn, gini_diffs, country, transfer_fn_name):
    old_data = np.asarray(old_data)

    traces = [
        go.Scatter(
            x = [0,1,2,3,4,5],
            y = [0] + list(old_data),
            name = "Actual (2013)"
        )
    ]

    for gd in gini_diffs:
        new_data = transfer_fn(old_data, gd)
        traces.append(go.Scatter(
            x = [0,1,2,3,4,5],
            y = [0] + list(new_data),
            name = "Gini increase: %.2f" % gd
        ))


    layout = go.Layout(
        xaxis=dict(title="Quintile #"),
        yaxis=dict(title="Fraction of income going to quintile"),
        title="Change in income distribution for 2013 %s (%s)" % (country, transfer_fn_name)
    )
    fig = go.Figure(data=traces, layout=layout)

    filename = "%s-%s.html" % (transfer_fn_name.lower().replace(" ", "-"), country)
    plotly.offline.plot(
        fig,
        filename=filename,
    )

US_2013_FRACTIONS = [
    0.051,
    0.103,
    0.154,
    0.227,
    0.464
]

SWEDEN_2013_FRACTIONS = [
    0.086,
    0.141,
    0.177,
    0.232,
    0.364
]

GINI_DIFFS = [0.01, 0.05, 0.1]

FRACTIONS = [
    ('US', US_2013_FRACTIONS),
    # ('Sweden', SWEDEN_2013_FRACTIONS)
]
TRANSFER_FNS = [
    (poorest_give_to_richest, "Poorest give to richest"),
    (poorest_give_to_everyone_equally, "Poorest give to everyone"),
    (everyone_gives_to_rich_equally, "Everyone give to rich")
]

for (country, data) in FRACTIONS:
    for (transfer_fn, transfer_fn_name) in TRANSFER_FNS:
        graph(data, transfer_fn, GINI_DIFFS, country, transfer_fn_name)
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