Visualizing the relationship between distributions and gini coefficient with Lorenz curves

distributions_gini_lorenz_curves.py

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt


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
    g = 0.5 * rmad
    return g


def lorenz(size, dist="normal", **params):
    if dist == "normal" and not params:
        params = {"loc": 0, "scale": 1}
    dist = getattr(np.random, dist)
    x = pd.Series(dist(size=size, **params)).abs().sort_values()

    g = gini(x)

    s = "; ".join([f"{k}={v}" for k, v in params.items()])
    plt.plot(
        x.rank() / x.shape[0], x.cumsum() / x.sum(),
        label=f"{dist.__name__}\nParams: {s}\nGini: {g:.2f}")
    plt.legend()


n = 1000
lorenz(n)
lorenz(n, loc=1, scale=1)
lorenz(n, loc=20, scale=1)
lorenz(n, loc=1, scale=0.1)
lorenz(n, dist="uniform")
lorenz(n, dist="poisson", lam=5)
lorenz(n, dist="poisson", lam=10)
lorenz(n, dist="negative_binomial", n=10, p=0.1)
lorenz(n, dist="negative_binomial", n=10, p=0.5)