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Hellinger Integral
In mathematics, the Hellinger integral is an integral introduced by that is a special case of the Kolmogorov integral. It is used to define the Hellinger distance In probability and statistics, the Hellinger distance (closely related to, although different from, the Bhattacharyya distance) is used to quantify the similarity between two probability distributions. It is a type of ''f''-divergence. The Hellin ... in probability theory. References * * * {{integral Definitions of mathematical integration ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kolmogorov Integral
In mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ..., the Kolmogorov integral (or Kolmogoroff integral) is a generalized integral introduced by including the Lebesgue–Stieltjes integral, the Burkill integral, and the Hellinger integral as special cases. The integral is a limit over a directed family of partitions, when the resulting limiting value is independent of the tags of each partition segment. References * * {{integral Definitions of mathematical integration ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hellinger Distance
In probability and statistics, the Hellinger distance (closely related to, although different from, the Bhattacharyya distance) is used to quantify the similarity between two probability distributions. It is a type of ''f''-divergence. The Hellinger distance is defined in terms of the Hellinger integral, which was introduced by Ernst Hellinger in 1909. It is sometimes called the Jeffreys distance. Definition Measure theory To define the Hellinger distance in terms of measure theory, let P and Q denote two probability measures on a measure space \mathcal that are absolutely continuous with respect to an auxiliary measure \lambda. Such a measure always exists, e.g \lambda = (P + Q). The square of the Hellinger distance between P and Q is defined as the quantity :H^2(P,Q) = \frac\displaystyle \int_ \left(\sqrt - \sqrt\right)^2 \lambda(dx). Here, P(dx) = p(x)\lambda(dx) and Q(dx) = q(x) \lambda(dx), i.e. p and q(x) = are the Radon–Nikodym derivatives of ''P'' and ''Q'' respe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Für Die Reine Und Angewandte Mathematik
''Crelle's Journal'', or just ''Crelle'', is the common name for a mathematics journal, the ''Journal für die reine und angewandte Mathematik'' (in English: ''Journal for Pure and Applied Mathematics''). History The journal was founded by August Leopold Crelle (Berlin) in 1826 and edited by him until his death in 1855. It was one of the first major mathematical journals that was not a proceedings of an academy. It has published many notable papers, including works of Niels Henrik Abel, Georg Cantor, Gotthold Eisenstein, Carl Friedrich Gauss and Otto Hesse. It was edited by Carl Wilhelm Borchardt from 1856 to 1880, during which time it was known as ''Borchardt's Journal''. The current editor-in-chief is Rainer Weissauer (Ruprecht-Karls-Universität Heidelberg) Past editors * 1826–1856 August Leopold Crelle * 1856–1880 Carl Wilhelm Borchardt * 1881–1888 Leopold Kronecker, Karl Weierstrass * 1889–1892 Leopold Kronecker * 1892–1902 Lazarus Fuchs * 1903–1928 Kurt Hens ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dover Publications
Dover Publications, also known as Dover Books, is an American book publisher founded in 1941 by Hayward and Blanche Cirker. It primarily reissues books that are out of print from their original publishers. These are often, but not always, books in the public domain. The original published editions may be scarce or historically significant. Dover republishes these books, making them available at a significantly reduced cost. Classic reprints Dover reprints classic works of literature, classical sheet music, and public-domain images from the 18th and 19th centuries. Dover also publishes an extensive collection of mathematical, scientific, and engineering texts. It often targets its reprints at a niche market, such as woodworking. Starting in 2015, the company branched out into graphic novel reprints, overseen by Dover acquisitions editor and former comics writer and editor Drew Ford. Most Dover reprints are photo facsimiles of the originals, retaining the original pagination and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |