Fluctuation in Grocery Sales by Brand: An Analysis Using Taylor’s Law

In recent years, Taylor’s law describing the power function relationship between the mean and standard deviation of certain phenomena has found an increasing number of applications. We studied the characteristics of Taylor’s law for branded product sales using point-of-sale (POS) data for brands sold in 72 grocery stores in the Greater Tokyo area. A previous study found that product sales follow Taylor’s law with a scaling exponent of 0.5 for low sales quantities and 1.0 for large sales quantities. In the current study, we observed Taylor’s law with cross-over for 54 product brands and estimated the value of the two coefficients in the theoretical curve to characterize the cross-over. The coefficients represent the fluctuations in the number of items purchased per consumer and the number of consumers in one store and in all stores. The estimated coefficients suggested the dependence of the features of Taylor’s law on the category to which the brands belong. We found that brands in the same category tend to share similar features under Taylor’s law. However, some brands exhibited specific features that differed from others in the same category. For example, for many brands in the Laundry Detergent and Instant Noodles categories, the number of customers purchasing the products in each store fluctuated significantly, whereas the number of purchased items per customer varied widely in the Japanese Tea category. In the coffee category, our results indicated that the degree of fluctuation in the number of purchasing customers largely depends on the brand.