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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 Stockholm University 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 Stockholm University. Also influenced by G. H. Hardy, Cramér's research led to a PhD in 1917 for his thesi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistics
Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of statistical survey, surveys and experimental design, experiments. When census data (comprising every member of the target population) cannot be collected, statisticians collect data by developing specific experiment designs and survey sample (statistics), samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Large Deviations Theory
In probability theory, the theory of large deviations concerns the asymptotic behaviour of remote tails of sequences of probability distributions. While some basic ideas of the theory can be traced to Laplace, the formalization started with insurance mathematics, namely ruin theory with Cramér and Lundberg. A unified formalization of large deviation theory was developed in 1966, in a paper by Varadhan. Large deviations theory formalizes the heuristic ideas of ''concentration of measures'' and widely generalizes the notion of convergence of probability measures. Roughly speaking, large deviations theory concerns itself with the exponential decline of the probability measures of certain kinds of extreme or ''tail'' events. Introductory examples An elementary example Consider a sequence of independent tosses of a fair coin. The possible outcomes could be heads or tails. Let us denote the possible outcome of the i-th trial by where we encode head as 1 and tail as 0. Now let ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stockholm
Stockholm (; ) is the Capital city, capital and List of urban areas in Sweden by population, most populous city of Sweden, as well as the List of urban areas in the Nordic countries, largest urban area in the Nordic countries. Approximately 1 million people live in the Stockholm Municipality, municipality, with 1.6 million in the Stockholm urban area, urban area, and 2.5 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. The city serves as the county seat of Stockholm County. Stockholm is the cultural, media, political, and economic centre of Sweden. The Stockholm region alone accounts for over a third of the country's Gros ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Kingman
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 that 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 and research ... [...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, the Erdős–Kac theorem on additive functions and the DDT theorem. 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Statistics
Mathematical statistics is the application of probability theory and other mathematical concepts to statistics, as opposed to techniques for collecting statistical data. Specific mathematical techniques that are commonly used in statistics 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 stati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistician
A statistician is a person who works with Theory, theoretical or applied statistics. The profession exists in both the private sector, 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. Overview 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 Actuary, actuaries, Applied mathematics, applied mathematicians, economists, data scientists, data analysts (predictive analytics), financial analysts, psychometricians, sociologists, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Actuary
An actuary is a professional with advanced mathematical skills who deals with the measurement and management of risk and uncertainty. These risks can affect both sides of the balance sheet and require investment management, asset management, liability (financial accounting), liability management, and valuation skills. Actuaries provide assessments of financial security systems, with a focus on their complexity, their mathematics, and their mechanisms. The name of the corresponding academic discipline is actuarial science. While the concept of insurance dates to antiquity, the concepts needed to scientifically measure and mitigate risks have their origins in 17th-century studies of probability and annuities. Actuaries in the 21st century require analytical skills, business knowledge, and an understanding of human behavior and information systems; actuaries use this knowledge to design programs that manage risk, by determining if the implementation of strategies proposed for mit ... [...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, mathematical structure, structure, space, Mathematical model, models, and mathematics#Calculus and analysis, change. History One of the earliest known mathematicians was Thales of Miletus (); 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's theorem. The number of known mathematicians grew when Pythagoras of Samos () 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 math ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sweden
Sweden, formally the Kingdom of Sweden, is a Nordic countries, Nordic country located on the Scandinavian Peninsula in Northern Europe. It borders Norway to the west and north, and Finland to the east. At , Sweden is the largest Nordic country by both area and population, and is the List of European countries by area, fifth-largest country in Europe. Its capital and largest city is Stockholm. Sweden has a population of 10.6 million, and a low population density of ; 88% of Swedes reside in urban areas. They are mostly in the central and southern half of the country. Sweden's urban areas together cover 1.5% of its land area. Sweden has a diverse Climate of Sweden, climate owing to the length of the country, which ranges from 55th parallel north, 55°N to 69th parallel north, 69°N. Sweden has been inhabited since Prehistoric Sweden, prehistoric times around 12,000 BC. The inhabitants emerged as the Geats () and Swedes (tribe), Swedes (), who formed part of the sea-faring peopl ... [...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 r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
