This paper introduces a new approach to estimating the text document complexity. Common readability indices are based on average length of sentences and words. In contrast to these methods, we propose to count the number of rare words occurring abnormally often in the document. We use the reference corpus of texts and the quantile approach in order to determine what words are rare, and what frequencies are abnormal. We construct a general text complexity model, which can be adjusted for the specific task, and introduce two special models. The experimental design is based on a set of thematically similar pairs of Wikipedia articles, labeled using crowdsourcing. The experiments demonstrate the competitiveness of the proposed approach.