Heaps' Law
Law
Let the number of vocabulary items in a corpus be $M$ and the number of tokens be $T$. Then $$ M = kT^{b} $$
Explanation
For an English corpus, the constants $k,b$ are usually said to appear roughly as $10 \le k \le 100$ and $b = 0.5$. Heaps’ law is not derived from a mathematical basis but is an empirically obtained law.
The formula may look extremely complicated at first glance, but taking the logarithm of both sides gives $\log M = \log k + b \log T$, and one can easily verify that there is a linear relationship as follows. $k$ represents the intercept and $b$ represents the slope.
