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Harald Cramér
Harald Cramér (; 25 September 1893 – 5 October 1985) was a Swedish mathematician, actuary, and statistician, specializing in mathematical statistics and probabilistic number theory. John Kingman described him as "one of the giants of statistical theory".Kingman 1986, p. 186. Biography Early life Harald Cramér was born in Stockholm, Sweden on 25 September 1893. Cramér remained close to Stockholm for most of his life. He entered the University of Stockholm as an undergraduate in 1912, where he studied mathematics and chemistry. During this period, he was a research assistant under the famous chemist, Hans von Euler-Chelpin, with whom he published his first five articles from 1913 to 1914. Following his lab experience, he began to focus solely on mathematics. He eventually began his work on his doctoral studies in mathematics which were supervised by Marcel Riesz at the University of Stockholm. Also influenced by G. H. Hardy, Cramér's research led to a PhD in 1917 for his th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stockholm
Stockholm () is the Capital city, capital and List of urban areas in Sweden by population, largest city of Sweden as well as the List of urban areas in the Nordic countries, largest urban area in Scandinavia. Approximately 980,000 people live in the Stockholm Municipality, municipality, with 1.6 million in the Stockholm urban area, urban area, and 2.4 million in the Metropolitan Stockholm, metropolitan area. The city stretches across fourteen islands where Mälaren, Lake Mälaren flows into the Baltic Sea. Outside the city to the east, and along the coast, is the island chain of the Stockholm archipelago. The area has been settled since the Stone Age, in the 6th millennium BC, and was founded as a city in 1252 by Swedish statesman Birger Jarl. It is also the county seat of Stockholm County. For several hundred years, Stockholm was the capital of Finland as well (), which then was a part of Sweden. The population of the municipality of Stockholm is expected to reach o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cramér–von Mises Criterion
In statistics the Cramér–von Mises criterion is a criterion used for judging the goodness of fit of a cumulative distribution function F^* compared to a given empirical distribution function F_n, or for comparing two empirical distributions. It is also used as a part of other algorithms, such as minimum distance estimation. It is defined as :\omega^2 = \int_^ _n(x) - F^*(x)2\,\mathrmF^*(x) In one-sample applications F^* is the theoretical distribution and F_n is the empirically observed distribution. Alternatively the two distributions can both be empirically estimated ones; this is called the two-sample case. The criterion is named after Harald Cramér and Richard Edler von Mises who first proposed it in 1928–1930. The generalization to two samples is due to Anderson. The Cramér–von Mises test is an alternative to the Kolmogorov–Smirnov test (1933). Cramér–von Mises test (one sample) Let x_1,x_2,\cdots,x_n be the observed values, in increasing order. Then th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Stockholm
Stockholm University ( sv, Stockholms universitet) is a public research university in Stockholm, Sweden, founded as a college in 1878, with university status since 1960. With over 33,000 students at four different faculties: law, humanities, social sciences, and natural sciences, it is one of the largest universities in Scandinavia. The institution is regarded as one of the top 100 universities in the world by the Academic Ranking of World Universities (ARWU).http://www.ulinks.com/topuniversities.htm top 200 Stockholm University was granted university status in 1960, making it the fourth oldest Swedish university. As with other public universities in Sweden, Stockholm University's mission includes teaching and research anchored in society at large. History The initiative for the formation of Stockholm University was taken by the Stockholm City Council. The process was completed after a decision in December 1865 regarding the establishment of a fund and a committee to "establish ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Kingman
__NOTOC__ Sir John Frank Charles Kingman (born 28 August 1939) is a British mathematician. He served as N. M. Rothschild and Sons Professor of Mathematical Sciences and Director of the Isaac Newton Institute at the University of Cambridge from 2001 until 2006, when he was succeeded by David Wallace. He is known for developing the mathematics of the Coalescent theory, a theoretical model of inheritance, which is fundamental to modern population genetics. Education and early life The grandson of a coal miner and son of a government scientist with a PhD in chemistry, Kingman was born in Beckenham, Kent, and grew up in the outskirts of London, where he attended Christ's College, Finchley, which was then a state grammar school. He was awarded a scholarship to read mathematics at Pembroke College, Cambridge, in 1956. On graduating in 1960, he began work on his PhD under the supervision of Peter Whittle, studying queueing theory, Markov chains and regenerative phenomena. Career a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probabilistic Number Theory
In mathematics, Probabilistic number theory is a subfield of number theory, which explicitly uses probability to answer questions about the integers and integer-valued functions. One basic idea underlying it is that different prime numbers are, in some serious sense, like independent random variables. This however is not an idea that has a unique useful formal expression. The founders of the theory were Paul Erdős, Aurel Wintner and Mark Kac during the 1930s, one of the periods of investigation in analytic number theory. Foundational results include the Erdős–Wintner theorem and the Erdős–Kac theorem on additive functions. See also *Number theory *Analytic number theory *Areas of mathematics *List of number theory topics *List of probability topics *Probabilistic method *Probable prime In number theory, a probable prime (PRP) is an integer that satisfies a specific condition that is satisfied by all prime numbers, but which is not satisfied by most composite numbers. Di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Statistics
Mathematical statistics is the application of probability theory, a branch of mathematics, to statistics, as opposed to techniques for collecting statistical data. Specific mathematical techniques which are used for this include mathematical analysis, linear algebra, stochastic analysis, differential equations, and measure theory. Introduction Statistical data collection is concerned with the planning of studies, especially with the design of randomized experiments and with the planning of surveys using random sampling. The initial analysis of the data often follows the study protocol specified prior to the study being conducted. The data from a study can also be analyzed to consider secondary hypotheses inspired by the initial results, or to suggest new studies. A secondary analysis of the data from a planned study uses tools from data analysis, and the process of doing this is mathematical statistics. Data analysis is divided into: * descriptive statistics - the part of st ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistician
A statistician is a person who works with theoretical or applied statistics. The profession exists in both the private and public sectors. It is common to combine statistical knowledge with expertise in other subjects, and statisticians may work as employees or as statistical consultants. Nature of the work According to the United States Bureau of Labor Statistics, as of 2014, 26,970 jobs were classified as ''statistician'' in the United States. Of these people, approximately 30 percent worked for governments (federal, state, or local). As of October 2021, the median pay for statisticians in the United States was $92,270. Additionally, there is a substantial number of people who use statistics and data analysis in their work but have job titles other than ''statistician'', such as actuaries, applied mathematicians, economist An economist is a professional and practitioner in the social science discipline of economics. The individual may also study, develop, and apply ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Actuary
An actuary is a business professional who deals with the measurement and management of risk and uncertainty. The name of the corresponding field is actuarial science. These risks can affect both sides of the balance sheet and require asset management, liability management, and valuation skills. Actuaries provide assessments of financial security systems, with a focus on their complexity, their mathematics, and their mechanisms. While the concept of insurance dates to antiquity, the concepts needed to scientifically measure and mitigate risks have their origins in the 17th century studies of probability and annuities. Actuaries of the 21st century require analytical skills, business knowledge, and an understanding of human behavior and information systems to design and manage programs that control risk. The actual steps needed to become an actuary are usually country-specific; however, almost all processes share a rigorous schooling or examination structure and take many years ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman mathematician recorded by history was Hypati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Guy Medal
The Guy Medals are awarded by the Royal Statistical Society in three categories; Gold, Silver and Bronze. The Silver and Bronze medals are awarded annually. The Gold Medal was awarded every three years between 1987 and 2011, but is awarded biennially as of 2019. They are named after William Guy. *The Guy Medal in Gold is awarded to fellows or others who are judged to have merited a signal mark of distinction by reason of their innovative contributions to the theory or application of statistics. *The Guy Medal in Silver is awarded to any fellow or, in exceptional cases, to two or more fellows in respect of a paper/papers of special merit communicated to the Society at its ordinary meetings, or in respect of a paper/papers published in any of the journals of the Society. General contributions to statistics may also be taken into account. *The Guy Medal in Bronze is awarded to fellows, or to non-fellows who are members of a section or a local group, in respect of a paper or papers rea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hermite Polynomials
In mathematics, the Hermite polynomials are a classical orthogonal polynomial sequence. The polynomials arise in: * signal processing as Hermitian wavelets for wavelet transform analysis * probability, such as the Edgeworth series, as well as in connection with Brownian motion; * combinatorics, as an example of an Appell sequence, obeying the umbral calculus; * numerical analysis as Gaussian quadrature; * physics, where they give rise to the eigenstates of the quantum harmonic oscillator; and they also occur in some cases of the heat equation (when the term \beginxu_\end is present); * systems theory in connection with nonlinear operations on Gaussian noise. * random matrix theory in Gaussian ensembles. Hermite polynomials were defined by Pierre-Simon Laplace in 1810, though in scarcely recognizable form, and studied in detail by Pafnuty Chebyshev in 1859. Chebyshev's work was overlooked, and they were named later after Charles Hermite, who wrote on the polynomials in 1864, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cramér's V
In statistics, Cramér's V (sometimes referred to as Cramér's phi and denoted as φ''c'') is a measure of association between two nominal variables, giving a value between 0 and +1 (inclusive). It is based on Pearson's chi-squared statistic and was published by Harald Cramér in 1946. Usage and interpretation φ''c'' is the intercorrelation of two discrete variablesSheskin, David J. (1997). Handbook of Parametric and Nonparametric Statistical Procedures. Boca Raton, Fl: CRC Press. and may be used with variables having two or more levels. φ''c'' is a symmetrical measure: it does not matter which variable we place in the columns and which in the rows. Also, the order of rows/columns doesn't matter, so φ''c'' may be used with nominal data types or higher (notably, ordered or numerical). Cramér's V may also be applied to goodness of fit chi-squared models when there is a 1 × ''k'' table (in this case ''r'' = 1). In this case ''k'' is taken as the number of optional ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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