改进的Bush-Wind准则对实验测量数据统计处理的信息量

Malaichuk Valentin, Klymenko Svitlana, Lysenko Nataliia
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引用次数: 0

摘要

使用有效的决策标准非常重要,特别是在确保信息安全方面。受控制的属性,如键盘手写特征、网络攻击强度等,都是由随机变量描述的,其分布规律通常是未知的。经典的非参数统计建议通过独立于分布类型的基于秩的同质性标准来比较随机变量的样本。利用Van der Warden位移准则和Klotz尺度准则,Bush和Wind提出了Bush-Wind联合准则。它是总体中两个正态均值和样本方差相等检验的渐近最优非参数统计量。本文考虑了如果由反高斯函数的近似形成的Van der Warden准则和Klotz准则被它们的类似物——logistic随机变量的逆函数所取代,那么检验两个实验测量样本的统计同质性假设的问题。通过计算实验,研究了基于logistic逆分布函数的经典Bush-Wind判据及其类似判据的信息量。本文提出的Bush-Wind准则的模拟与经典准则的不同之处在于在保持效率的同时降低了计算复杂度。通过对logistic、Rayleigh和指数随机变量样本进行计算实验得到的样本同质性识别的经验概率表明,该准则具有非参数性、高灵敏度和在实验数据有限的情况下应用该准则的可能性。改进的Bush-Wind判据具有信息量大的特点,可推荐用于实验测量的统计处理。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Informativeness of statistical processing of experimental measurements by the modified Bush-Wind criterion
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.
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