Heaps' law
In linguistics, Heaps' law (also called Herdan's law) is an empirical law which describes the number of distinct words in a document (or set of documents) as a function of the document length (so called type-token relation). It can be formulated as

  
    
      
        
          V
          
            R
          
        
        (
        n
        )
        =
        K
        
          n
          
            β
          
        
      
    
    {\displaystyle V_{R}(n)=Kn^{\beta }}
  

where VR is the number of distinct words in an instance text of size n. K and β are free parameters determined empirically. With English text corpora, typically K is between 10 and 100, and β is between 0.4 and 0.6. The law is frequently attributed to Harold Stanley Heaps, but was originally discovered by Gustav Herdan (1960). Under mild assumptions, the Herdan–Heaps law is asymptotically equivalent to Zipf's law concerning the frequencies of individual words within a text.