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Thorvald N. Thiele
Thorvald Nicolai Thiele (24 December 1838 – 26 September 1910) was a Danish astronomer and director of the Copenhagen Observatory. He was also an actuary and mathematician, most notable for his work in statistics, interpolation and the three-body problem. Thiele made notable contributions to the statistical study of random time series and introduced the cumulants and likelihood functions, and was considered to be one of the greatest statisticians of all time by Ronald Fisher. In the early 1900s he also developed and proposed a generalisation of approval voting to multiple winner elections called sequential proportional approval voting, which was briefly used for party lists in Sweden when proportional representation was introduced in 1909. Thiele also was a founder and Mathematical Director of the Hafnia Insurance Company and led the founding of the Danish Society of Actuaries. It was through his insurance work that he came into contact with fellow mathematician Jørgen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Copenhagen
Copenhagen ( or .; da, København ) is the capital and most populous city of Denmark, with a proper population of around 815.000 in the last quarter of 2022; and some 1.370,000 in the urban area; and the wider Copenhagen metropolitan area has 2,057,142 people. Copenhagen is on the islands of Zealand and Amager, separated from Malmö, Sweden, by the Øresund strait. The Øresund Bridge connects the two cities by rail and road. Originally a Viking fishing village established in the 10th century in the vicinity of what is now Gammel Strand, Copenhagen became the capital of Denmark in the early 15th century. Beginning in the 17th century, it consolidated its position as a regional centre of power with its institutions, defences, and armed forces. During the Renaissance the city served as the de facto capital of the Kalmar Union, being the seat of monarchy, governing the majority of the present day Nordic region in a personal union with Sweden and Norway ruled by th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sequential Proportional Approval Voting
Sequential proportional approval voting (SPAV) or reweighted approval voting (RAV) is an electoral system that extends the concept of approval voting to a multiple winner election. It is a simplified version of proportional approval voting. Proposed by Danish statistician Thorvald N. Thiele in the early 1900s, it was used (with adaptations for party lists) in Sweden for a short period from 1909-1921, and was replaced by a cruder "party-list" style system as it was easier to calculate. Description Sequential Proportional Approval Voting (SPAV) uses Approval Voting ballots to elect multiple winners equitably by selecting a candidate in each round and then reweighing the approvals for the subsequent rounds. Each ballot is assigned a value equal to the reciprocal of one more than the number of candidates approved on that ballot who have been designated as elected. Each ballot is counted at its current value as a vote for all continuing candidates approved on that ballot. The candi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thiele's Interpolation Formula
In mathematics, Thiele's interpolation formula is a formula that defines a rational function f(x) from a finite set of inputs x_i and their function values f(x_i). The problem of generating a function whose graph passes through a given set of function values is called interpolation. This interpolation formula is named after the Danish mathematician Thorvald N. Thiele. It is expressed as a continued fraction, where ρ represents the reciprocal difference In mathematics, the reciprocal difference of a finite sequence of numbers (x_0, x_1, ..., x_n) on a function f(x) is defined inductively by the following formulas: :\rho_1(x_1, x_2) = \frac :\rho_2(x_1, x_2, x_3) = \frac + f(x_2) :\rho_n(x_1,x_ ...: : f(x) = f(x_1) + \cfrac References * Finite differences Articles with example ALGOL 68 code Interpolation {{mathanalysis-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Least Squares
The method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems (sets of equations in which there are more equations than unknowns) by minimizing the sum of the squares of the residuals (a residual being the difference between an observed value and the fitted value provided by a model) made in the results of each individual equation. The most important application is in data fitting. When the problem has substantial uncertainties in the independent variable (the ''x'' variable), then simple regression and least-squares methods have problems; in such cases, the methodology required for fitting errors-in-variables models may be considered instead of that for least squares. Least squares problems fall into two categories: linear or ordinary least squares and nonlinear least squares, depending on whether or not the residuals are linear in all unknowns. The linear least-squares problem occurs in statistical regress ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kalman Filter
For statistics and control theory, Kalman filtering, also known as linear quadratic estimation (LQE), is an algorithm that uses a series of measurements observed over time, including statistical noise and other inaccuracies, and produces estimates of unknown variables that tend to be more accurate than those based on a single measurement alone, by estimating a joint probability distribution over the variables for each timeframe. The filter is named after Rudolf E. Kálmán, who was one of the primary developers of its theory. This digital filter is sometimes termed the ''Stratonovich–Kalman–Bucy filter'' because it is a special case of a more general, nonlinear filter developed somewhat earlier by the Soviet mathematician Ruslan Stratonovich. In fact, some of the special case linear filter's equations appeared in papers by Stratonovich that were published before summer 1960, when Kalman met with Stratonovich during a conference in Moscow. Kalman filtering has numerous te ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gram–Charlier Series
The Gram–Charlier A series (named in honor of Jørgen Pedersen Gram and Carl Charlier), and the Edgeworth series (named in honor of Francis Ysidro Edgeworth) are series that approximate a probability distribution in terms of its cumulants. The series are the same; but, the arrangement of terms (and thus the accuracy of truncating the series) differ. The key idea of these expansions is to write the characteristic function of the distribution whose probability density function is to be approximated in terms of the characteristic function of a distribution with known and suitable properties, and to recover through the inverse Fourier transform. Gram–Charlier A series We examine a continuous random variable. Let \hat be the characteristic function of its distribution whose density function is , and \kappa_r its cumulants. We expand in terms of a known distribution with probability density function , characteristic function \hat, and cumulants \gamma_r. The density is generall ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Founders Of Statistics
Statistics is the theory and application of mathematics to the scientific method including hypothesis generation, experimental design, sampling, data collection, data summarization, estimation, prediction and inference from those results to the population from which the experimental sample was drawn. This article lists statisticians who have been instrumental in the development of theoretical and applied statistics. Founders of departments of statistics The role of a department of statistics is discussed in a 1949 article by Harold Hotelling, which helped to spur the creation of many departments of statistics. See also * List of statisticians * History of statistics * Timeline of probability and statistics * List of people considered father or mother of a scientific field References External links * * * * * StatProbnbsp;– peer-reviewed encyclopedia sponsored by statistics and probability societies {{DEFAULTSORT:Founders Of Statistics History of probabil ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1586 Thiele
Events * January 18 – The 7.9 Tenshō earthquake strikes the Chubu region of Japan, triggering a tsunami and causing at least 8,000 deaths. * June 16 – The deposed and imprisoned Mary, Queen of Scots, recognizes Philip II of Spain as her heir. * July 6 – The Treaty of Berwick is signed between Queen Elizabeth I of England and King James VI of Scotland. * July 21 – English explorer Thomas Cavendish begins the first deliberately planned circumnavigation of the globe. * September 20– 21 – Execution of the Babington Plotters: The 14 men convicted of a plot (uncovered on July 17) to murder Queen Elizabeth and replace her with Mary, Queen of Scots, are hanged, drawn and quartered (the first seven being disembowelled before death) in St Giles Field, London. * September 22 – Battle of Zutphen: Spanish troops defeat the Dutch rebels and their English allies. English poet and courtier Sir Philip Sidney is mortally wounded. * October 15&nd ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
843 Nicolaia
843 Nicolaia is a main-belt asteroid An asteroid is a minor planet of the inner Solar System. Sizes and shapes of asteroids vary significantly, ranging from 1-meter rocks to a dwarf planet almost 1000 km in diameter; they are rocky, metallic or icy bodies with no atmosphere. ... discovered by Danish astronomer H. Thiele on 30 September 1916. It was a lost asteroid for 65 years before being rediscovered by Astronomisches Rechen-Institut at Heidelberg in 1981. The asteroid is orbiting the Sun with a period of 3.44 years. References External links * * 000843 Discoveries by Holger Thiele Named minor planets 19160930 {{beltasteroid-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Holger Thiele
Holger Thiele (September 25, 1878 – June 5, 1946) was a Danish American astronomer and discoverer of minor planets and comets. He was the son of Thorvald Nicolai Thiele (1838–1910), the noted Danish astronomer, actuary and mathematician, after whom the main-belt asteroid 1586 Thiele is named. Holger Thiele is credited by the Minor Planet Center with the discovery of 4 numbered asteroids during 1914–1916. He also discovered the comet C/1906 V1 and calculated the orbits of other comets. He worked at Hamburg-Bergedorf Observatory at Bergedorf, in Hamburg, Germany. In 1912, he immigrated to the United States. In 1917, he started working as a fellow for the University of California at Lick Observatory The Lick Observatory is an astronomical observatory owned and operated by the University of California. It is on the summit of Mount Hamilton, in the Diablo Range just east of San Jose, California, United States. The observatory is managed by t ..., near San Jose, Califo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jørgen Pedersen Gram
Jørgen Pedersen Gram (27 June 1850 – 29 April 1916) was a Danish actuary and mathematician who was born in Nustrup, Duchy of Schleswig, Denmark and died in Copenhagen, Denmark. Important papers of his include ''On series expansions determined by the methods of least squares'', and ''Investigations of the number of primes less than a given number''. The mathematical method that bears his name, the Gram–Schmidt process, was first published in the former paper, in 1883. For number theorists his main fame is the series for the Riemann zeta function (the leading function in Riemann's exact prime-counting function). Instead of using a series of logarithmic integrals, Gram's function uses logarithm powers and the zeta function of positive integers. It has recently been supplanted by a formula of Ramanujan that uses the Bernoulli numbers directly instead of the zeta function. In control theory, the Gramian or Gram matrix is an important contribution named after him. The C ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Insurance
Insurance is a means of protection from financial loss in which, in exchange for a fee, a party agrees to compensate another party in the event of a certain loss, damage, or injury. It is a form of risk management, primarily used to hedge against the risk of a contingent or uncertain loss. An entity which provides insurance is known as an insurer, insurance company, insurance carrier, or underwriter. A person or entity who buys insurance is known as a policyholder, while a person or entity covered under the policy is called an insured. The insurance transaction involves the policyholder assuming a guaranteed, known, and relatively small loss in the form of a payment to the insurer (a premium) in exchange for the insurer's promise to compensate the insured in the event of a covered loss. The loss may or may not be financial, but it must be reducible to financial terms. Furthermore, it usually involves something in which the insured has an insurable interest established by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
