Pareto law of the expenditure of a person in convenience stores

TL;DR

This study analyzes a large dataset of receipts from convenience stores, revealing a power-law distribution in individual expenditures, significant economic inequality among customers, and the Pareto principle's applicability to sales distribution.

Contribution

It provides empirical evidence of power-law expenditure distribution and quantifies customer inequality using the Lorenz curve and Gini coefficient.

Findings

Expenditure density follows a fat-tailed power law.

Top 25% and 2% of customers contribute 80% and 25% of sales.

Gini coefficient of 0.70 indicates strong inequality.

Abstract

We study the statistical laws of the expenditure of a person in convenience stores by analysing around 100 million receipts. The density function of expenditure exhibits a fat tail that follows a power law. We observe the Pareto principle where both the top 25% and 2% of the customers account for 80% and 25% of the store's sales, respectively. Using the Lorenz curve, the Gini coefficient is estimated to be 0.70; this implies a strong economic inequality.