Informativeness of statistical processing of experimental measurements by the modified Bush-Wind criterion

Abstract

The use of effective decision-making criteria is very important, especially when it comes to ensuring information security. Controlled attributes, such as keyboard handwriting charac-teristics, intensity of network attacks, and many others, are described by random variables whose distribution laws are usually unknown. Classical nonparametric statistics suggests comparing samples of random variables by rank-based homogeneity criteria that are inde-pendent of the type of distribution. Using the Van der Warden shift criterion and the Klotz scale criterion, Bush and Wind proposed the combined Bush-Wind criterion. It is an asymp-totically optimal nonparametric statistic for equal testing of two normal means and sample variances in a population. The article considers the problem of testing the hypothesis of sta-tistical homogeneity of two experimental measurement samples if the Van der Warden and Klotz criteria, which are formed by approximations of the inverse Gaussian functions, are re-placed by their analogues - the inverse functions of logistic random variables. Computational experiments are carried out and the informativeness of the classical Bush-Wind criterion and its analog, which is formed on the logistic inverse distribution function, is investigated. The analog of the Bush-Wind criterion proposed in this paper differs from the classical criterion by reducing computational complexity while maintaining efficiency. The empirical probabili-ties of recognizing the homogeneity of samples, obtained by conducting computational ex-periments for samples of logistic, Rayleigh and exponential random variables, indicate non-parametricity, high sensitivity and the possibility of applying the criterion in conditions of limited experimental data. The modified Bush-Wind criterion is characterized by high infor-mation content and can be recommended for statistical processing of experimental measure-ments.