INFORMATIVENESS OF THE CRITERIA OF STATISTICAL HOMOGENEITY OF SAMPLES OF EXPONENTIAL MEASUREMENTS

Abstract

In the paper, examines the statistical homogeneity of samples of independent random variables with an exponential distribution. It is known that one of the main characteristics of the reliability of rocket and space systems is the law of distribution of its resource. However, an exponential distribution is used to determine unexpected failures. This paper aimed to conduct computational experiments to verify the requirement that the measured parameters be statistically homogeneous. In practice, probability theory most often uses parametric verification criteria based on the assumption that statistical data obey a normal distribution. However, in some cases, such assumptions lead to erroneous conclusions. In this paper, nonparametric criteria, such as the Spearman rank test and the Shirahate test, which incorporate information about the state of technical objects, were used to verify homogeneity. A distinctive feature of these criteria is their flexibility, which allows their use in problems where the conditions for applying parametric methods are not met. The theory suggests that the Shirahate test, which is characterized by the formation of complex ranks, is more informative. This article explored the informative value of statistical homogeneity in random variable samples for three types of probability distribution functions with small sample sizes. After constructing experimental measurement sample models, computational experiments and a visual and graphical analysis of the histograms of the Spearman and Shirahate tests were conducted. In accordance with the problem conditions, an analogue of the Shirahate test was tested for a sample length of n = 10, yielding an empirical probability of P*(n) = 0,9504, confirming the hypothesis of statistical homogeneity for random variable samples with an exponential distribution.