An alternative method to test scale invariance

Abstract

We introduce an alternative method that is simple and can be used to test scale invariance or self-similarity in any types of data, irrespective of their distributions. Our method is based on estimating the Lorenz curve and the Kolmogorov–Smirnov test. This alternative method could be used as a preliminary screening before investigating further which types of distributions would fit the actual observations. • We introduce a simple method to test scale invariance, regardless of data distributions. • Our method is based on estimating the Lorenz curve and the Kolmogorov–Smirnov test. • This alternative method could serve as an initial screening before investigating further which types of distributions would fit the actual data.

Keywords

• Scale-free
• Self-similarity
• Rank-size distribution
• Income and wealth
• Lorenz curve
• Kolmogorov–Smirnov test