Zipf’s Law

Zipf’s Law is a statistical principle that describes the distribution of elements in various natural, social, and man-made systems.

Postings size use Zipf’s Law: $f(k;s,N)=\frac{1}{{\sum }_{n=1}^N(1/n^s)}$

• $N$ is the number of elements
• $k$ is the rank, anywhere between $1$ and $N$
• $s$ is the characteristic exponent

What does the rank mean here?

rank(k) refers to the position of an element in a sorted list based on its frequency of occurrence.

Zipf’s Law: (also) linear in log-log space

• A few elements occur very frequently
• Many elements occur very infrequently
• Ohh, it’s like the 80-20 Rule - https://www.youtube.com/watch?v=fCn8zs912OE&t=253s&ab_channel=Vsauce