Power-law correlation between sales and the number of products in the database of supermarkets

Abstract

The database "Nikkei supermarket POS data" contains the daily sales data which are collectedfrom about 300 supermarkets in Japan. Using this database, wefind a power-law correlationbetween the number of products and sales of supermarkets. This means that sales of supermarketsbecome larger not linearly but in power law as the number of products increase. Furthermore,we observe that the power-law exponent does not change largely over the last 10 years. Thiscorrelation is, therefore, thought to be an universal law.