Do individuals in this population have higher incomes than those in that population?
Conference
65th ISI World Statistics Congress 2025
Format: IPS Abstract - WSC 2025
Keywords: "stochastic dominance"
Session: IPS 784 - Statistical Advances Across Diverse Complex Data Landscapes
Wednesday 8 October 2 p.m. - 3:40 p.m. (Europe/Amsterdam)
Abstract
The question in the title is usually answered by comparing a global parameter like the mean income (there are other options, but they suffer from similar, though not as important, problems). However, the global parameters do no take individuals into account: it is quite easy to construct two populations, A and B, of arbitrary size, such that the mean income in A is higher than the mean income in B and everyone in A but one have lower incomes than everyone in B.
A possible solution to this problem is to use the stochastic order, since it is based on comparing percentiles, or, roughly speaking, pairs of ordered individuals. Unfortunately, this order is rarely satisfied (note that a single individual makes this order fail). In this talk, I will introduce several indices to measure how far the distribution of incomes in population A is to be stochastically larger than the distribution of incomes in B.
The talk includes the analysis of some real data sets and it is based on the paper Barrio, E. del, Cuesta-Albertos, J.A. and Matran, C. (2024),
Some indices to measure departures from stochastic order.
Preprint, http://arxiv.org/abs/1804.02905.