In this study, we show how Luhn's claim about the degree of importance of a word in a document can be related to information retrieval. His basic idea is transformed into z -scores as the weights of terms for the purpose of modeling terra frequency (If) within documents. The Luhn-based models represented in this paper are considered as the TF component of proposed TF x IDF weighing schemes. Moreover, the final term weighting functions appropriate for the TF x IDF weighting scheme are applied to TREC-6, -7, and -8 databases. The experimental results show relevance to Luhn's claim by having high mean average precision (MAP) for the terms with frequencies around the mean frequency of terms within a document. On the other hand, the weighting, which significantly discriminates the importance between low/high frequencies and medium frequencies, degrades the retrieval performance. Therefore, any weighting scheme (TF) that is directly proportional to If has a probability of high retrieval performance, if this can optimally indicate the difference of the importance regarding tf values and also optimally eliminate the terms that have high frequencies.