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Thomas Royen
Thomas Royen (born 6 July 1947) is a retired German professor of statistics who has been affiliated with the University of Applied Sciences Bingen. Royen came to prominence in the spring of 2017 for a relatively simple proof for the Gaussian Correlation Inequality (GCI), a conjecture that originated in the 1950s, which he had published three years earlier without much recognition.Royen's proof of the Gaussian correlation inequality, arXiv:1512.08776/ref> A proof of this conjecture, which lies at the intersection of geometry, probability theory and statistics, had eluded top experts for decades. Life Youth, studies and private life Royen was born in 1947 to Paul Royen, a professor with the institute for inorganic chemistry at the Goethe University Frankfurt and Elisabeth Royen, also a chemist. From 1966 to 1971, he studied mathematics and physics at his father's university and the University of Freiburg. After graduating, he worked as a tutor at the University of Freiburg, before ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frankfurt Am Main
Frankfurt, officially Frankfurt am Main (; Hessian dialects, Hessian: , "Franks, Frank ford (crossing), ford on the Main (river), Main"), is the most populous city in the States of Germany, German state of Hesse. Its 791,000 inhabitants as of 2022 make it the List of cities in Germany by population, fifth-most populous city in Germany. Located on its namesake Main (river), Main River, it forms a continuous conurbation with the neighboring city of Offenbach am Main and Frankfurt Rhein-Main Regional Authority, its urban area has a population of over 2.3 million. The city is the heart of the larger Rhine-Main metropolitan region, which has a population of more than 5.6 million and is Germany's Metropolitan regions in Germany, second-largest metropolitan region after the Rhine-Ruhr region. Frankfurt's central business district, the Bankenviertel, lies about northwest of the geographic centre of the EU, geographic center of the EU at Gadheim, Lower Franconia. Like France and Franc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Schwalbach Am Taunus
Schwalbach am Taunus, a town in the Main-Taunus-Kreis district, in Hesse, Germany, population about 14,000, is a dormitory town to Frankfurt, situated some 11 km east of Schwalbach. There is evidence of human habitation dating back to Neolithic times, and recorded history going back to 781 AD. Until the end of the Second World War, it was a farming village, but in the post-war era it expanded rapidly and became economically linked to Frankfurt. Schwalbach was granted ''Gemeinde'' (municipal) status in 1970. Geography Location The town is located between Taunus mountain range, about 10 km from the Kleiner Feldberg (825 m), and the River Main. Although the centre of the city of Frankfurt am Main is about 10 km from Schwalbach centre, the most southerly tip of Schwalbach (agricultural land) shares a one kilometre common boundary with Frankfurt (along the A66 Autobahn). The original settlement, now known as ''Alt-Schwalbach'', was built at the confluen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ArXiv
arXiv (pronounced " archive"—the X represents the Greek letter chi ⟨χ⟩) is an open-access repository of electronic preprints and postprints (known as e-prints) approved for posting after moderation, but not peer review. It consists of scientific papers in the fields of mathematics, physics, astronomy, electrical engineering, computer science, quantitative biology, statistics, mathematical finance and economics, which can be accessed online. In many fields of mathematics and physics, almost all scientific papers are self-archived on the arXiv repository before publication in a peer-reviewed journal. Some publishers also grant permission for authors to archive the peer-reviewed postprint. Begun on August 14, 1991, arXiv.org passed the half-million-article milestone on October 3, 2008, and had hit a million by the end of 2014. As of April 2021, the submission rate is about 16,000 articles per month. History arXiv was made possible by the compact TeX file ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quanta Magazine
''Quanta Magazine'' is an editorially independent online publication of the Simons Foundation covering developments in physics, mathematics, biology and computer science Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to practical disciplines (includin .... ''Undark Magazine'' described ''Quanta Magazine'' as "highly regarded for its masterful coverage of complex topics in science and math." The science news aggregator ''RealClearScience'' ranked ''Quanta Magazine'' first on its list of "The Top 10 Websites for Science in 2018." In 2020, the magazine received a National Magazine Award for General Excellence from the American Society of Magazine Editors for its "willingness to tackle some of the toughest and most difficult topics in science and math in a language that is accessible to the lay reader without condes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
LaTeX
Latex is an emulsion (stable dispersion) of polymer microparticles in water. Latexes are found in nature, but synthetic latexes are common as well. In nature, latex is found as a milky fluid found in 10% of all flowering plants (angiosperms). It is a complex emulsion that coagulates on exposure to air, consisting of proteins, alkaloids, starches, sugars, oils, tannins, resins, and gums. It is usually exuded after tissue injury. In most plants, latex is white, but some have yellow, orange, or scarlet latex. Since the 17th century, latex has been used as a term for the fluid substance in plants, deriving from the Latin word for "liquid". It serves mainly as defense against herbivorous insects. Latex is not to be confused with plant sap; it is a distinct substance, separately produced, and with different functions. The word latex is also used to refer to natural latex rubber, particularly non- vulcanized rubber. Such is the case in products like latex gloves, latex ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Donald Richards (statistician)
Donald St. P. Richards (born 1955, in Mandeville, Jamaica) is an American statistician conducting research on multivariate statistics, zonal polynomials, distance correlation, total positivity, and hypergeometric functions of matrix argument. He currently serves as a distinguished professor of statistics at the Pennsylvania State University, and is a Fellow of the Institute of Mathematical Statistics and a Fellow of the American Mathematical Society. Richards obtained his PhD in 1978 at the University of the West Indies, where the statistician Rameshwar D. Gupta was his doctoral advisor. In 1999, he was elected a Fellow of the Institute of Mathematical Statistics. In 2012, he was elected a Fellow of the American Mathematical Society. Personal life Richards became an American citizen in 1990. He was married to Mercedes Richards Mercedes Tharam Richards (Kingston, 14 May 1955 – Hershey, 3 February 2016), née Davis, was a Jamaican astronomy and astrophysics professor. Her ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Olive Jean Dunn
Olive Jean Dunn (1 September 1915 – 12 January 2008) was an American mathematician and statistician, and professor of biostatistics at the University of California Los Angeles (UCLA). She described methods for computing confidence intervals and also codified the Bonferroni correction's application to confidence intervals. She authored the textbook ''Basic Statistics: A Primer for the Biomedical Sciences'' in 1977. Education and career Dunn studied mathematics at the UCLA, earning a BA in 1936 and an MA in 1951. She was awarded a PhD in mathematics in 1956 at UCLA, supervised by Paul G. Hoel. The title of Dunn's doctoral dissertation was ''Estimation problems for dependent regression''. In 1956, she was appointed assistant professor of statistics at Iowa State College. Dunn returned to UCLA in 1959 as assistant professor of biostatistics and assistant professor of preventive medicine and health, later becoming full professor and serving in that role until her retirement ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Laplace Transform
In mathematics, the Laplace transform, named after its discoverer Pierre-Simon Laplace (), is an integral transform that converts a function of a real variable (usually t, in the ''time domain'') to a function of a complex variable s (in the complex frequency domain, also known as ''s''-domain, or s-plane). The transform has many applications in science and engineering because it is a tool for solving differential equations. In particular, it transforms ordinary differential equations into algebraic equations and convolution into multiplication. For suitable functions ''f'', the Laplace transform is the integral \mathcal\(s) = \int_0^\infty f(t)e^ \, dt. History The Laplace transform is named after mathematician and astronomer Pierre-Simon, marquis de Laplace, who used a similar transform in his work on probability theory. Laplace wrote extensively about the use of generating functions in ''Essai philosophique sur les probabilités'' (1814), and the integral form of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ArXiv
arXiv (pronounced " archive"—the X represents the Greek letter chi ⟨χ⟩) is an open-access repository of electronic preprints and postprints (known as e-prints) approved for posting after moderation, but not peer review. It consists of scientific papers in the fields of mathematics, physics, astronomy, electrical engineering, computer science, quantitative biology, statistics, mathematical finance and economics, which can be accessed online. In many fields of mathematics and physics, almost all scientific papers are self-archived on the arXiv repository before publication in a peer-reviewed journal. Some publishers also grant permission for authors to archive the peer-reviewed postprint. Begun on August 14, 1991, arXiv.org passed the half-million-article milestone on October 3, 2008, and had hit a million by the end of 2014. As of April 2021, the submission rate is about 16,000 articles per month. History arXiv was made possible by the compact TeX file ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gamma Distribution
In probability theory and statistics, the gamma distribution is a two- parameter family of continuous probability distributions. The exponential distribution, Erlang distribution, and chi-square distribution are special cases of the gamma distribution. There are two equivalent parameterizations in common use: #With a shape parameter k and a scale parameter \theta. #With a shape parameter \alpha = k and an inverse scale parameter \beta = 1/ \theta , called a rate parameter. In each of these forms, both parameters are positive real numbers. The gamma distribution is the maximum entropy probability distribution (both with respect to a uniform base measure and a 1/x base measure) for a random variable X for which E 'X''= ''kθ'' = ''α''/''β'' is fixed and greater than zero, and E n(''X'')= ''ψ''(''k'') + ln(''θ'') = ''ψ''(''α'') − ln(''β'') is fixed (''ψ'' is the digamma function). Definitions The parameterization with ''k'' and ''θ'' appears to be more common ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chi-square Distribution
In probability theory and statistics, the chi-squared distribution (also chi-square or \chi^2-distribution) with k degrees of freedom is the distribution of a sum of the squares of k independent standard normal random variables. The chi-squared distribution is a special case of the gamma distribution and is one of the most widely used probability distributions in inferential statistics, notably in hypothesis testing and in construction of confidence intervals. This distribution is sometimes called the central chi-squared distribution, a special case of the more general noncentral chi-squared distribution. The chi-squared distribution is used in the common chi-squared tests for goodness of fit of an observed distribution to a theoretical one, the independence of two criteria of classification of qualitative data, and in confidence interval estimation for a population standard deviation of a normal distribution from a sample standard deviation. Many other statistical tests also ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multivariate Distribution
Given two random variables that are defined on the same probability space, the joint probability distribution is the corresponding probability distribution on all possible pairs of outputs. The joint distribution can just as well be considered for any given number of random variables. The joint distribution encodes the marginal distributions, i.e. the distributions of each of the individual random variables. It also encodes the conditional probability distributions, which deal with how the outputs of one random variable are distributed when given information on the outputs of the other random variable(s). In the formal mathematical setup of measure theory, the joint distribution is given by the pushforward measure, by the map obtained by pairing together the given random variables, of the sample space's probability measure. In the case of real-valued random variables, the joint distribution, as a particular multivariate distribution, may be expressed by a multivariate cumulati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
