Fig 1.
Time series of delivery quantities for a single product, rice ball at a store (red), sales quantities (blue), discard quantities (green), total customer numbers (black).
Table 1.
Product categories and the coefficients of the variation (σN/μN) for each week’s totals for all stores.
Fig 2.
(a) Cumulative distribution of time interval (minutes) in semi-log plot: daytime on weekday (red solid line), daytime on non-weekday (blue solid line), evening on weekday (red dashed line), evening on non-weekday (blue dashed line). (b) Autocorrelation of time interval.
Fig 3.
(a),(b) Sales-quantity time series and distribution of 1product, 1store, each day of the week. (c),(d) Sales-quantity time series and distribution of 1product, all stores within the city, each day of the week. In (b),(d), green line shows a Poisson distribution whose mean is the same as the mean of real data. In (d), blue line is a Gaussian distribution whose mean is the same as the mean of real data and the standard deviation is 0.1 times of the mean of real data. In (a),(c), green and blue dashed lines represent the standard deviations of (b),(d), respectively, and black line is the mean of real data. (e) Relationship between mean and standard deviation of sales quantities in the soft drinks category. Regarding plot points, for each day of week: circle, weekly totals: cross, 1 product on 1 store: red, all products on 1 store: blue, 1 product within locality: green, all products within locality: magenta, 1 product within city: cyan, all products within city; black. Black solid line shows , and black dashed line shows σ = 0.15μ. (f) Means of (e) with error bars given by the standard deviation. Two red triangles indicate mean and standard deviation of (a) and (c).
Fig 4.
Relationship between mean and standard deviation of sales quantities by category: cheese (red) and hair-styling (blue).
Solid, dashed and dotted line show , σ = 0.26μ, and σ = 0.05μ respectively.
Fig 5.
(a) Relationship between mean and standard deviation of customer-quantities time series for the soft drink category. Regarding plot points, for each day of week: circle, weekly totals: cross, on 1 store: red, within 1 locality: green, within city: blue. Black solid line shows , and black dashed line shows σN = 0.10μN. (b) Mean of (a).
Fig 6.
Relationship between mean and standard deviation of customer-numbers time series by category: cheese (red) and hair-styling (blue).
Solid, dashed and dotted line show , σN = 0.19μN, and σN = 0.06μN respectively.
Fig 7.
Comparison of actual data and theory.
(a) Japanese sake (rice wine), (b) Soft drinks, (c) Eggs, (d) Tissues, (e) Magazines, (f) Stamps. Solid and dashed line show Eq (15), the crossover value Am respectively.
Fig 8.
Comparison of reproducibility for two item categories: cheese (red) and hair-styling (blue).
Two solid line show Eq (15) and dashed lines indicate crossover value Am respectively. Plots are same as in Fig 4.
Fig 9.
Cumulative distribution of quantities by a purchase.
(1)Magazines, (2)Eggs, (3)Salads and soup, (4)Gelled items, (5)Instant noodles, (6)Tissues, (7)Soft drinks, (8)Stamps. Dashed line shows x−2
Fig 10.
Scaling law in the magazines category.
Solid and dashed lines show Eq (15), crossover value Am respectively.
Fig 11.
Scaling laws in the magazines category considering the date of sale of each magazine.
(a),(b) Results on date of sale. (c),(d) Results on a day after the date of sale. Solid and dashed line show Eq (15), crossover value Am respectively. (b) is the mean of (a), (d) is the mean of (c).