import math


def theil_l_index(distribution):
    """Theil's L Index is sensitive to differences at the lower end of the
    distribution (small incomes).

    Args:
        distribution (list): wealth distribution of the population

    Returns:
        (float): Theil's L Index (TL), inequality of wealth distribution
            0 <= TL < +inf
            TL = 0, perfect equality
    """
    n = len(distribution)
    mean_amount = sum(distribution) / n
    epsilon = 0
    for amount in distribution:
        epsilon += math.log(amount / mean_amount)
    return - epsilon / n