The Gini coefficient and negative income: A probabilistic approach

Karim Kilani (1)

1 LIRSA - Laboratoire interdisciplinaire de recherche en sciences de l'action

This paper discusses the Gini index when a mass of individuals in the population sharing the wealth suffers a loss. This question has been addressed in the statistical framework while here it is treated from a probabilistic point of view, which allows us to be as exhaustive as possible. The assumptions are the most general ones on probability distributions. We determine a condition on the Lorenz function that generates a Gini index that exceeds unity. We construct an adjusted Gini index, i.e. one that remains within limits between zero and one, according to a method advocated in the statistical framework. After having recovered the recommended index in the statistical case, we apply the method to continuous distributions, namely the uniform distribution and the generalized Pareto distribution, thus showing the operability of the method.

Keywords: Adjusted Gini index; Lorenz function; Negative income; Quantile function JEL classification. C43

Domains: Quantitative Finance [q-fin]

Karim Kilani. The Gini coefficient and negative income: A probabilistic approach. 2022. ⟨hal-03911502⟩