Processing complexity in exacting probability distributions of symmetrical additively partitioned statistics and application area of limit distributions

Annotation: In the paper the authors consider application of the frequency method to calculate the exact probability distributions of symmetrical additively partitioned statistics, and analyze its computational and time complexity. The values of boundary parameters are investigated, for which, at present, could be calculated the exact distributions using the frequency method. The possibilities of exact distributions calculation with the help of the frequency method and the trivial method of full enumeration are compared. Besides, the analyses is done for the values of boundary parameters of texts, for which it is now possible to calculate exact distributions. The application possibilities for exact and limit probability distributions of statistics are considered, and could be used further for fitting criterion creation within symbolic data analysis.

Keywords: probability, statistics, criterion, exact distribution, limit distribution, computational complexity of method, performance of multiprocessor computer system