Real-time studying of statistic distributions of non-parametric goodness-of-fit tests when testing complex hypotheses

A random number of vehicles crossed a transverse line of a highway during an arbitrary interval of time and a random number of vehicles situated on an arbitrary part of the highway at a fixed instant of time form a complicated stochastic dependence. In case of bad weather and bad road conditions the spatial intervals between the neighbouring vehicles at a fixed instant of time (a spatial characteristic of the flow) are dependent and have different probability distributions. Under these conditions, the intervals between moments of crossing the transverse line of the highway by the consecutive vehicles (a temporal characteristic of the flow) are also dependent and have different probability distributions. In this paper some probabilistic regularities in motion of this kind of traffic flows are researched. Real-time studying of statistic distributions of non-parametric goodness-of-fit tests when testing complex hypotheses In present work, a " real-time " ability to simulate and research the distributions of tests statistics in the course of testing the complex goodness-of-fit hypothesis (for distributions with estimated parameters) is implemented by the use of parallel computing. It makes it possible to make correct statistical inferences even in those situations when the distribution of the test statistic is unknown (before the testing procedure starts). tests) and nonparametric tests (Ansari-Bradley's, Mood's, Siegel-Tukey's, Capon's and Klotz's tests) have been considered. Distributions of classical tests statistics have been investigated under violation of assumption that samples are normally distributed. The comparative analysis of power of classical tests with power of nonparametric tests has been carried out. Tables of percentage points for Cochran's test have been made for distributions which are different from normal. Software, that allows us to apply tests correctly, has been developed. Keywords: homogeneity of variance test, power of test. The algorithm generating the sample of random numbers of defined distribution and numerical characteristics (expectation, dispersion, etc.) is considered. The high accuracy of algorithm working on sample modeling is shown. The general principle of sample generation allows assigning the given approach in a category of random-numbers generation algorithms that combining such algorithms in group of " precision random-numbers generator ". This paper presents the investigation results for the Nikulin-Rao-Robson (NRR) chi-square type test. The distributions of the NRR test statistic have been investigated by means of computer simulation technique depending on the sample size, censoring distribution, proportion of censoring and number of intervals. Simulation studies of chi-square test statistic distributions …