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In the present paper an attempt has been made to determine the mathematical model for the frequencies of occurrence of letters in the corpora, in the word types of the corpora and in the initial positions of words of the corpora while both the word tokens and word types have been taken into account. In the current study corpora written in American English have been used by the selection of the entities from ‘The Open American National Corpus (OANC)’.

Mathematical modeling of the frequencies of letters for their occurrence in corpora, words (types) and in the initial positions of words of corpora