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Index Of Dispersion
In probability theory and statistics, the index of dispersion, dispersion index, coefficient of dispersion, relative variance, or variance-to-mean ratio (VMR), like the coefficient of variation, is a normalized measure of the dispersion of a probability distribution: it is a measure used to quantify whether a set of observed occurrences are clustered or dispersed compared to a standard statistical model. It is defined as the ratio of the variance \sigma^2 to the mean \mu, :D = . It is also known as the Fano factor, though this term is sometimes reserved for ''windowed'' data (the mean and variance are computed over a subpopulation), where the index of dispersion is used in the special case where the window is infinite. Windowing data is frequently done: the VMR is frequently computed over various intervals in time or small regions in space, which may be called "windows", and the resulting statistic called the Fano factor. It is only defined when the mean \mu is non-zero, and is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Theory
Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms of probability, axioms. Typically these axioms formalise probability in terms of a probability space, which assigns a measure (mathematics), measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space. Any specified subset of the sample space is called an event (probability theory), event. Central subjects in probability theory include discrete and continuous random variables, probability distributions, and stochastic processes (which provide mathematical abstractions of determinism, non-deterministic or uncertain processes or measured Quantity, quantities that may either be single occurrences or evolve over time in a random fashion). Although it is no ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eccentricity (mathematics)
In mathematics, the eccentricity of a Conic section#Eccentricity, conic section is a non-negative real number that uniquely characterizes its shape. One can think of the eccentricity as a measure of how much a conic section deviates from being circular. In particular: * The eccentricity of a circle is 0. * The eccentricity of a non-circular ellipse is between 0 and 1. * The eccentricity of a parabola is 1. * The eccentricity of a hyperbola is greater than 1. * The eccentricity of a pair of Line (geometry), lines is \infty. Two conic sections with the same eccentricity are similarity (geometry), similar. Definitions Any conic section can be defined as the Locus (mathematics), locus of points whose distances to a point (the focus) and a line (the directrix) are in a constant ratio. That ratio is called the ''eccentricity'', commonly denoted as . The eccentricity can also be defined in terms of the intersection of a plane and a Cone (geometry), double-napped cone associated with ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
South Dakota
South Dakota (; Sioux language, Sioux: , ) is a U.S. state, state in the West North Central states, North Central region of the United States. It is also part of the Great Plains. South Dakota is named after the Dakota people, Dakota Sioux tribe, which comprises a large portion of the population—with nine Indian reservation, reservations in the state—and has historically dominated the territory. South Dakota is the List of U.S. states and territories by area, 17th-largest by area, the List of U.S. states and territories by population, fifth-least populous, and the List of U.S. states and territories by population density, fifth-least densely populated of the List of U.S. states, 50 United States. Pierre, South Dakota, Pierre is the List of capitals in the United States, state capital, and Sioux Falls, South Dakota, Sioux Falls, with a population of about 213,900, is South Dakota's List of cities in South Dakota, most populous city. The state is bisected by the Missouri Ri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
New York (state)
New York, also called New York State, is a U.S. state, state in the northeastern United States. Bordered by New England to the east, Canada to the north, and Pennsylvania and New Jersey to the south, its territory extends into both the Atlantic Ocean and the Great Lakes. New York is the List of U.S. states and territories by population, fourth-most populous state in the United States, with nearly 20 million residents, and the List of U.S. states and territories by area, 27th-largest state by area, with a total area of . New York has Geography of New York (state), a varied geography. The southeastern part of the state, known as Downstate New York, Downstate, encompasses New York City, the List of U.S. cities by population, most populous city in the United States; Long Island, with approximately 40% of the state's population, the nation's most populous island; and the cities, suburbs, and wealthy enclaves of the lower Hudson Valley. These areas are the center of the expansive New ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Iowa
Iowa ( ) is a U.S. state, state in the upper Midwestern United States, Midwestern region of the United States. It borders the Mississippi River to the east and the Missouri River and Big Sioux River to the west; Wisconsin to the northeast, Illinois to the east and southeast, Missouri to the south, Nebraska to the west, South Dakota to the northwest, and Minnesota to the north. Iowa is the List of U.S. states and territories by area, 26th largest in total area and the List of U.S. states and territories by population, 31st most populous of the List of states and territories of the United States, 50 U.S. states, with a population of 3.19 million. The state's List of capitals in the United States, capital, List of cities in Iowa, most populous city, and largest List of metropolitan statistical areas, metropolitan area fully located within the state is Des Moines, Iowa, Des Moines. A portion of the larger Omaha–Council Bluffs metropolitan area, Omaha, Nebraska, metropolitan area ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Annals Of Mathematical Statistics
The ''Annals of Mathematical Statistics'' was a peer-reviewed statistics journal published by the Institute of Mathematical Statistics from 1930 to 1972. It was superseded by the '' Annals of Statistics'' and the '' Annals of Probability''. In 1938, Samuel Wilks became editor-in-chief of the ''Annals'' and recruited a remarkable editorial staff: Fisher, Neyman, Cramér, Hotelling, Egon Pearson Egon Sharpe Pearson (11 August 1895 – 12 June 1980) was one of three children of Karl Pearson and Maria, née Sharpe, and, like his father, a British statistician. Career Pearson was educated at Winchester College and Trinity College ..., Georges Darmois, Allen T. Craig, Deming, von Mises, H. L. Rietz, and Shewhart. References External links ''Annals of Mathematical Statistics''at Project Euclid Statistics journals Probability journals {{statistics-journal-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paul G
Paulo George Marques João (born March 31), better known by his stage name Paul G, is an Angolan urban pop and R&B singer-songwriter, producer and dancer. He began his career as a founding member of Angola's first worldly known rap group South Side Posse (SSP) alongside Big Nelo, Jeff Brown, and Kudi. Later, Paul G went on to produce and guide the career of Bruna Tatiana, making her the first contestant from Angola in the hit real life television show Big Brother Africa. The success of his productions and collaborations with other artists gave him the opportunity to visit the United States of America, where he met with music producer H. Gil Ingles, a founding member of XPOSURE Entertainment. That sealed his career as a solo artist with the production of the debut album "Transition". In 2009, Paul G released his debut album Transition, which contained the Kora-nominated hit "Freaking Me Out" that features hip-hop artist Alashus (aka C1), and the original version of MTV Base nomi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arthur Roy Clapham
Arthur Roy Clapham (24 May 1904 – 18 December 1990), was a British botanist. Born in Norwich and educated at Downing College, Cambridge, Clapham worked at Rothamsted Experimental Station as a crop physiologist (1928–30), and then took a teaching post in the botany department at Oxford University. He was Professor of Botany at Sheffield University 1944–69 and vice chancellor of the university during the 1960s. He coauthored the ''Flora of the British Isles'', which was the first, and for several decades the only, comprehensive flora of the British Isles published in 1952 and followed by new editions in 1962 and 1987. In response to a request from Arthur Tansley, he coined the term ecosystem in the early 1930s. Early life and education Clapham was born in Norwich to George Clapham, an elementary school teacher and Dora Margaret Clapham, ''née'' Harvey. He was the oldest of three children and the only boy. He attended the City of Norwich School, where he sat the Cambridge ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lexis Ratio
The Lexis ratioLexis W (1877) Zur Theorie Der Massenerscheinungen in Der Menschlichen Gesellschaft. is used in statistics as a measure which seeks to evaluate differences between the statistical properties of random mechanisms where the outcome is two-valued — for example "success" or "failure", "win" or "lose". The idea is that the probability of success might vary between different sets of trials in different situations. This ratio is not much used currently having been largely replaced by the use of the chi-squared test in testing for the homogeneity of samples. This measure compares the between-set variance of the sample proportions (evaluated for each set) with what the variance should be if there were no difference between in the true proportions of success across the different sets. Thus the measure is used to evaluate how data compares to a fixed-probability-of-success Bernoulli distribution. The term "Lexis ratio" is sometimes referred to as ''L'' or ''Q'', where :L^ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Random Walk
In mathematics, a random walk, sometimes known as a drunkard's walk, is a stochastic process that describes a path that consists of a succession of random steps on some Space (mathematics), mathematical space. An elementary example of a random walk is the random walk on the integer number line \mathbb Z which starts at 0, and at each step moves +1 or −1 with equal probability. Other examples include the path traced by a molecule as it travels in a liquid or a gas (see Brownian motion), the search path of a foraging animal, or the price of a fluctuating random walk hypothesis, stock and the financial status of a gambler. Random walks have applications to engineering and many scientific fields including ecology, psychology, computer science, physics, chemistry, biology, economics, and sociology. The term ''random walk'' was first introduced by Karl Pearson in 1905. Realizations of random walks can be obtained by Monte Carlo Simulation, Monte Carlo simulation. Lattice random ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brownian Motion
Brownian motion is the random motion of particles suspended in a medium (a liquid or a gas). The traditional mathematical formulation of Brownian motion is that of the Wiener process, which is often called Brownian motion, even in mathematical sources. This motion pattern typically consists of Randomness, random fluctuations in a particle's position inside a fluid sub-domain, followed by a relocation to another sub-domain. Each relocation is followed by more fluctuations within the new closed volume. This pattern describes a fluid at thermal equilibrium, defined by a given temperature. Within such a fluid, there exists no preferential direction of flow (as in transport phenomena). More specifically, the fluid's overall Linear momentum, linear and Angular momentum, angular momenta remain null over time. The Kinetic energy, kinetic energies of the molecular Brownian motions, together with those of molecular rotations and vibrations, sum up to the caloric component of a fluid's in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Hypothesis Testing
A statistical hypothesis test is a method of statistical inference used to decide whether the data provide sufficient evidence to reject a particular hypothesis. A statistical hypothesis test typically involves a calculation of a test statistic. Then a decision is made, either by comparing the test statistic to a Critical value (statistics), critical value or equivalently by evaluating a p-value, ''p''-value computed from the test statistic. Roughly 100 list of statistical tests, specialized statistical tests are in use and noteworthy. History While hypothesis testing was popularized early in the 20th century, early forms were used in the 1700s. The first use is credited to John Arbuthnot (1710), followed by Pierre-Simon Laplace (1770s), in analyzing the human sex ratio at birth; see . Choice of null hypothesis Paul Meehl has argued that the epistemological importance of the choice of null hypothesis has gone largely unacknowledged. When the null hypothesis is predicted by the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
