Data Science Basics: Power Laws and Distributions

Power laws are a powerful class of tool which can help us better understand the world around us. Also known as scaling laws, power laws essentially imply that a small number of occurrences of some phenomena are frequent, or very common, while a large number of of occurrences of the same phenomena are infrequent, or very rare; the exact relationship between these relative frequencies differ between power law distributions. Some of the wide array of naturally occurring and man made phenomena which power laws are able to describe include income disparities, word frequencies of a given language, city sizes, website sizes, magnitudes of earthquakes, book sales rankings, and surname popularity. The all-knowing Wikipedia more formally defines a power law as follows: [A] power law is a functional relationship between two…

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