Wyniki wyszukiwania - BazTech

1

A Kolmogorov-Smirnov Test for r Samples

Böhm W., Hornik K.

Fundamenta Informaticae

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2012

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Vol. 117, nr 1-4

103-125

EN

We consider the problem of testing whether r ≥2 samples are drawn from the same continuous distribution F(x). The test statistic we will study in some detail is defined as the maximum of the circular differences of the empirical distribution functions, a generalization of the classical 2-sample Kolmogorov-Smirnov test to r ≥2 independent samples. For the case of equal sample sizes we derive the exact null distribution by counting lattice paths confined to stay in the scaled alcove Ar of the affineWeyl group Ar-1. This is done using a generalization of the classical reflection principle. By a standard diffusion scaling we derive also the asymptotic distribution of the test statistic in terms of a multivariate Dirichlet series. When the sample sizes are not equal the reflection principle no longer works, but we are able to establish a weak convergence result even in this case showing that by a proper rescaling a test statistic based on a linear transformation of the circular differences of the empirical distribution functions has the same asymptotic distribution as the test statistic in the case of equal sample sizes.

2

Plane angle measurements in polycrystalline metal structure

Kasprzyk A., Matusiewicz P., Czarski A., Wiencek K.

Metallurgy and Foundry Engineering

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2004

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Vol. 30, No 1

79-84

EN

The distributions of plane angles for real polycrystalline structure of titanium were calculated. The measurement of each angle was carried by three persons independently. Individual results were used for making three plane angle distribution. The Kolmogorov - Smirnov test was used to compare these distributions. The correlation and regression analysis for the angle measurement results of observer pairs was performed.

PL

Wyznaczono rozkłady kątów płaskich dla rzeczywistej struktury polikrystalicznej tytanu. Pomiaru każdego kąta dokonywały trzy osoby, niezależnie od siebie. Uzyskane indywidualne wyniki pomiarów posłużyły do wyznaczenia trzech rozkładów kątów płaskich oraz ich parametrów. Z kolei uśrednione dla każdego kąta wartości posłużyły do testowania hipotezy o ich normalności. Dla wyników pomiarów poszczególnych par obserwatorów wyznaczono współczynniki korelacji i regresji.

3

Robust region merging for motion based segmentation using the Kolmogorov-Smirnov test

Broekhoven M., Hupkens T., Hendriks E., Patras I.

Image Processing & Communications

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2000

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Vol. 6, no 3-4

27-34

EN

This paper addresses the problem of segmenting image sequences into moving objects. The proposed method uses a bottom-up approach and uses an indirect method to estimate the motion parameters of the initial regions. These regions have been created using the watershed algorithm. The motion of the regions have been modelled by a four parameter affine model and have been estimated by using a robust method, which diminishes the influence of wrongly estimated displacement or optical flow vectors (outliers). The similarity measure between two adjacent regions is computed through a non-parametric statistical test (the Kolmogorov-Smirnov test) as proposed by Moscheni [1] with some important modifications. The algorithm iterates between a motion estimation step and a region merging step until some stopping criterion has been reached. The results indicate that the method is well suited to obtain a correct segmentation of real image sequences.