many commonly used statistical methods require that the population distribution be nearly normal. unfortunately, in some papers the one-sample kolmogorov-smirnov test has been used for testing normality while the assumptions of applying this test are not satisfied. to conduct this test, it is assumed that the population distribution is fully specified. in practical situation where the mean and ...

Signal detection performance in cognitive radio architecture is enhanced by the cooperation of sensing detectors if the fading and shadowing effects exist on the channel. A cooperative spectrum sensing technique in cognitive radio networks based on two-sample Kolmogorov-Smirnov test is proposed in this paper and proposed sensing scheme is examined under Rician fading channel. The performance of...

This article considers the CUSUM-based (cumulative sum) test for a change point in a time series. In the case of testing for a mean shift, the traditional Kolmogorov–Smirnov test statistic involves a consistent long-run variance estimator, which is needed to make the limiting null distribution free of nuisance parameters. The commonly used lag-window type long-run variance estimator requires to...

This article presents a derivation of the distribution of the Kolmogorov–Smirnov, Cramer–von Mises, and Anderson–Darling test statistics in the case of exponential sampling when the parameters are unknown and estimated from sample data for small sample sizes via maximum likelihood.

The minimum complexity or minimum description-length criterion developed by Kolmogorov, Rissanen, Wallace, So&in, and others leads to consistent probability density estimators. These density estimators are defined to achieve the best compromise between likelihood and simplicity. A related issue is the compromise between accuracy of approximations and complexity relative to the sample size. An i...

Similarly to his great predecessors P. L. Tschebyshev and A. M. Lyapunov, the academician A. N. Kolmogorov (25.04.1903– 20.10.1987) was not only a universal mathematician, proposing and developing fruitful ideas, he also readily answered challenges presented to him in his capacity as an applied mathematician. He had an amazing ability to get to the root of a problem, to determine fundamental is...