This paper deals with the problem of author identification. The Common N-Grams (CNG) method [6] is a language-independent profile-based approach with good results in many author identification experiments so far. A variation of this approach is presented based on new distance measures that are quite stable for large profile length values. Special emphasis is given to the degree upon which the effectiveness of the method is affected by the available training text samples per author. Experiments based on text samples on the same topic from the Reuters Corpus Volume 1 are presented using both balanced and imbalanced training corpora. The results show that CNG with the proposed distance measures is more accurate when only limited training text samples are available, at least for some of the candidate authors, a realistic condition in author identification problems.