#### Event Title

Decomposition of the Gini Index into Non-Overlapping Subgroups

#### Session Number

O06

#### Advisor(s)

Michael McAsey, Bradley University

Libin Mou, Bradley University

#### Location

B-116

#### Start Date

28-4-2016 8:00 AM

#### End Date

28-4-2016 8:25 AM

#### Disciplines

Mathematics

#### Abstract

The Gini index is a single number that attempts to measure inequality. However, this common measure of inequality fails to describe how unequal different parts of a population are, and only provides a view of the population as a whole. We investigated the relationship between the measures for specific groups and the measure of the total population. We constructed a formula that gives the Gini index as a function of the indices of the smaller groups within a population, given that they do not overlap. This formula expresses the Gini index as a sum of the Gini indices of the subgroups multiplied by coefficients plus a constant term. The coefficients which we use to write the Gini index in this formula are composed of the number of values in each subgroup and the totals of each subgroup, as well as the number of values in the distribution and the total of the distribution. Our formula leads to another form of the overall Gini index by considering each member in the population as a subgroup. The relationship has been researched in the past, and we provide a new formulation and direct proof.

Decomposition of the Gini Index into Non-Overlapping Subgroups

B-116

The Gini index is a single number that attempts to measure inequality. However, this common measure of inequality fails to describe how unequal different parts of a population are, and only provides a view of the population as a whole. We investigated the relationship between the measures for specific groups and the measure of the total population. We constructed a formula that gives the Gini index as a function of the indices of the smaller groups within a population, given that they do not overlap. This formula expresses the Gini index as a sum of the Gini indices of the subgroups multiplied by coefficients plus a constant term. The coefficients which we use to write the Gini index in this formula are composed of the number of values in each subgroup and the totals of each subgroup, as well as the number of values in the distribution and the total of the distribution. Our formula leads to another form of the overall Gini index by considering each member in the population as a subgroup. The relationship has been researched in the past, and we provide a new formulation and direct proof.