The article proposes a method of compiling statistics of the most common trigrams in texts of different lengths, comparing several small passages with general statistics, and on the basis of the obtained data, a minimum adequate sample is proposed. The method for verification of hypotheses is proposed to test the distribution laws by using different criteria. The statistical processing of the results of the quantitative analysis of trigrams is presented. Calculation of metrological parameters for estimation of unknown parameters of the trigram distribution is performed. In the quantitative analysis, not an infinitely large number of definitions but several independent definitions is made, that is, having a sample (total sample) of 5-6 options. The conditions for the choice of linguistic models, as well as the following types of linguistic-mathematical models are described: ideal and reproducing. The methodological functions of applied linguistics are reviewed. The special sections of mathematics used in linguistic theory and practice are reviewed. The possibility of extracting the sample from the log-normal general population is statistically tested as a complex non-parametric hypothesis. The test was carried out using Kolmogorov's criterion.
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