Miguel A. Sordo, Héctor M. Ramos, Carmen D. Ramosm (2007)
SORT
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We examine the conditions under which unanimous poverty rankings of income distributions can be obtained for a general class of poverty indices. The "per-capita income gap" and the Shorrocks and Thon poverty measures are particular members of this class. The conditions of dominance are stated in terms of comparisons of the corresponding TIP curves and areas.
Mariusz Paradowski (2015)
International Journal of Applied Mathematics and Computer Science
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Over a century of research has resulted in a set of more than a hundred binary association measures. Many of them share similar properties. An overview of binary association measures is presented, focused on their order equivalences. Association measures are grouped according to their relations. Transformations between these measures are shown, both formally and visually. A generalization coefficient is proposed, based on joint probability and marginal probabilities. Combining association...
Robert Susmaga, Izabela Szczech (2015)
International Journal of Applied Mathematics and Computer Science
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The paper presents visualization techniques for interestingness measures. The process of measure visualization provides useful insights into different domain areas of the visualized measures and thus effectively assists their comprehension and selection for different knowledge discovery tasks. Assuming a common domain form of the visualized measures, a set of contingency tables, which consists of all possible tables having the same total number of observations, is constructed. These...
Alice Fiaschi (2008)
ESAIM: Control, Optimisation and Calculus of Variations
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Rate-independent evolution for material models with nonconvex elastic energies is studied without any spatial regularization of the inner variable; due to lack of convexity, the model is developed in the framework of Young measures. An existence result for the quasistatic evolution is obtained in terms of compatible systems of Young measures. We also show as this result can be equivalently reformulated with probabilistic language and leads to the description of the quasistatic evolution...
Dejian Tian, Long Jiang (2016)
Open Mathematics
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In this paper, we introduce some definitions of uncertainty orders for random vectors in a sublinear expectation space. We all know that, under some continuity conditions, each sublinear expectation 𝔼 has a robust representation as the supremum of a family of probability measures. We describe uncertainty orders from two different viewpoints. One is from sublinear operator viewpoint. After giving definitions such as monotonic orders, convex orders and increasing convex orders, we use...
Artur Bartoszewicz (1978)
Colloquium Mathematicae
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Eckhard Liebscher (2017)
Dependence Modeling
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The aim of the present paper is to develop and examine association coefficients which can be helpfully applied in the framework of regression analysis. The construction of the coeffiecients is connected with the well-known Spearman coeffiecient and extensions of it (see Liebscher [5]). The proposed coeffiecient measures the discrepancy between the data points and a function which is strictly increasing on one interval and strictly decreasing in the remaining domain.We prove statements...
Stanisław Szufla (2001)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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K. P. S. Bhaskara Rao, B. V. Rao (1979)
Colloquium Mathematicae
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Una Radojičić, Klaus Nordhausen, Hannu Oja (2020)
Applications of Mathematics
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Partial orderings and measures of information for continuous univariate random variables with special roles of Gaussian and uniform distributions are discussed. The information measures and measures of non-Gaussianity including the third and fourth cumulants are generally used as projection indices in the projection pursuit approach for the independent component analysis. The connections between information, non-Gaussianity and statistical independence in the context of independent component...
K. P. S. Bhaskara Rao, B. V. Rao (1975)
Colloquium Mathematicae
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Václav Remeš, Michal Haindl (2018)
Kybernetika
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A survey of local image contrast measures is presented and a new contrast measure for measuring the local contrast of regions of interest is proposed. The measures validation is based on the gradual objective contrast decreasing on medical test images in both grayscale and color. The performance of the eleven most frequented contrast measures is mutually compared and their robustness to different types of image degradation is analyzed. Since the contrast measures can be both global,...