Estimating a Structural Distribution Function by Grouping

The concept of a structural distribution function originates from linguistics. Let M denote the size of the vocabulary of an author and consider a text of this author that contains n words. Every choice of a word in the text from the vocabulary can be seen as the realization of a multinomial random vector. The whole text consists of a sequence of such choices X = (X (i) 1,M , . . . , X (i) M,M), i = 1, 2, . . . , n , which are assumed to be independent. So each X is Multinomial(1, p1,M , p2,M , . . . , pM,M) distributed, where p1,M , p2,M , . . . , pM,M denote the cell probabilities. In linguistics the vector of those word probabilities is viewed as a characteristic of the author. More specifically one is interested in estimating the so called structural distribution function.