The article discusses the open problem of authorship identification, when the analyzed text can be written by one of known authors or an unknown author. For identification, the impostor method with a large number of external texts is used. A practical approach to achieve the minimum arithmetic mean of errors of the first and second kinds based on joint selection of the values of two parameters of the method is proposed. The experimental results are given for texts in Russian and Arabic. In the experimental results, the minimum arithmetic mean of errors is achieved when the length of the texts-impostors is equal to the average length of the texts of the author’s collections.