Authors A. K. Melnikov
Month, Year 08, 2018 @en
Index UDC 519.224.22
DOI 10.23683/2311-3103-2018-8-114-135
Abstract In the paper we consider application of limit and exact approximations of statistics probability distributions for the problem of selection of texts with specific statistical properties. For selection of texts with equiprobable distribution of their symbols we use the statistical fitting criterion. Here, as a standard distribution of the test statistic we use its various approximations. As extreme approximations we use limit distributions, and as exact approximations we use ∆exact distributions. The difference between ∆exact distributions and exact distributions does not exceed the specified ∆. We present the calculation results of ∆exact distributions, show their variations from the values of limit distributions for different statistics. We consider the notion of processing efficiency for selection of equiprobable texts, which shows the part of wrong selected texts. We compare the processing efficiency for exact and limit approximations of standard distributions of test statistics. We have proved that the processing efficiency does not decreasing, but in many cases it is increasing, if the exact approximation is used instead of the extreme one. To compare the statistical criteria which are based on the same test statistic and different standard distributions, we introduce a concept of the distribution relative efficiency which shows the fold increase of the number of wrong selected texts for the criterion of one or another distribution used as a standard distribution. We show the functional connection between the concepts “processing efficiency” and “relative efficiency” of distributions. Owing to availability of high-performance computing facilities, which can be used for calculation of ∆exact distributions for such parameters as the length and capacity of the text alphabet, we have proved the statement about relative efficiency of distributions. Owing to the statement it is possible to select a standard distribution of the criterion (with the highest processing efficiency) from the set of distributions of the test statistic. In addition we give the examples of the values of relative efficiency for exact and extreme approximations.

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Keywords Probability; test statistics, criterion; standard distribution; exact distribution; limit distribution; processing efficiency; relative efficiency of distribution; computational complexity of method; performance of multiprocessor computer system.
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