The exact rank-frequency function and size-frequency function of N-grams and N-word phrases with applications

Abstract

N-grams are generalized words consisting of N consecutive symbols (letters), as they are used in a text. N-word phrases are general concepts consisting of N consecutive words, also as used in a text. Given the rank-frequency function of single letters (i.e. 1-grams) or of single words (i.e. 1-word phrases) being Zipfian, we determine in this paper the exact rank-frequency function (i.e. the occurrence of N-grams or N-word phrases on each rank) and size-frequency distribution (i.e. the density of N-grams or N-word phrases on each occurrence density) of these N-grams and N-word phrases. This paper distinguishes itself from other ones on this topic by allowing no approximations in the calculations. This leads to an intricate rank-frequency function for N-grams and N-word phrases (as we knew before from unpublished calculations) but leads surprisingly, to a very simple size-frequency function f(N) for N-grams or N-word phrases.