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Variance-to-mean Ratio
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, an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Theory
Probability theory 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. Typically these axioms formalise probability in terms of a probability space, which assigns a 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. Central subjects in probability theory include discrete and continuous random variables, probability distributions, and stochastic processes (which provide mathematical abstractions of non-deterministic or uncertain processes or measured quantities that may either be single occurrences or evolve over time in a random fashion). Although it is not possible to perfectly predict random events, much can be said about their behavior. Two major results in probab ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eccentricity (mathematics)
In mathematics, the eccentricity of a conic section is a non-negative real number that uniquely characterizes its shape. More formally two conic sections are similar if and only if they have the same eccentricity. 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 zero. * The eccentricity of an ellipse which is not a circle is greater than zero but less than 1. * The eccentricity of a parabola is 1. * The eccentricity of a hyperbola is greater than 1. * The eccentricity of a pair of lines is \infty Definitions Any conic section can be defined as the 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 double-napped cone associated with the conic section. If the cone is orient ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
New York (state)
New York, officially the State of New York, is a state in the Northeastern United States. It is often called New York State to distinguish it from its largest city, New York City. With a total area of , New York is the 27th-largest U.S. state by area. With 20.2 million people, it is the fourth-most-populous state in the United States as of 2021, with approximately 44% living in New York City, including 25% of the state's population within Brooklyn and Queens, and another 15% on the remainder of Long Island, the most populous island in the United States. The state is bordered by New Jersey and Pennsylvania to the south, and Connecticut, Massachusetts, and Vermont to the east; it has a maritime border with Rhode Island, east of Long Island, as well as an international border with the Canadian provinces of Quebec to the north and Ontario to the northwest. New York City (NYC) is the most populous city in the United States, and around two-thirds of the state's popul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Iowa
Iowa () is a state in the Midwestern region of the United States, bordered by the Mississippi River to the east and the Missouri River and Big Sioux River to the west. It is bordered by six states: 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. During the 18th and early 19th centuries, Iowa was a part of French Louisiana and Spanish Louisiana; its state flag is patterned after the flag of France. After the Louisiana Purchase, people laid the foundation for an agriculture-based economy in the heart of the Corn Belt. In the latter half of the 20th century, Iowa's agricultural economy transitioned to a diversified economy of advanced manufacturing, processing, financial services, information technology, biotechnology, and green energy production. Iowa is the 26th most extensive in total area and the 31st most populous of the 50 U.S. states, with a popul ... [...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, Georges Darmois, Allen T. Craig, Deming, von Mises, H. L. Rietz Henry Lewis Rietz (24 August 1875, Gilmore, Ohio – 7 December 1943, Iowa City, Iowa) was an American mathematician, actuarial scientist, and statistician, who was a leader in the development of statistical theory. He became the first president o ..., and Shewhart. References {{reflist External links Annals of Mathematical Statistics at Project Euclid Statistics journals Probability journals ... [...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] |
Journal Of The Royal Statistical Society, Series C
The ''Journal of the Royal Statistical Society'' is a peer-reviewed scientific journal of statistics. It comprises three series and is published by Wiley for the Royal Statistical Society. History The Statistical Society of London was founded in 1834, but would not begin producing a journal for four years. From 1834 to 1837, members of the society would read the results of their studies to the other members, and some details were recorded in the proceedings. The first study reported to the society in 1834 was a simple survey of the occupations of people in Manchester, England. Conducted by going door-to-door and inquiring, the study revealed that the most common profession was mill-hands, followed closely by weavers. When founded, the membership of the Statistical Society of London overlapped almost completely with the statistical section of the British Association for the Advancement of Science. In 1837 a volume of ''Transactions of the Statistical Society of London'' were ... [...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 Cambridg ... [...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 is a random process that describes a path that consists of a succession of random steps on some 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 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. Lattice random walk A popular random walk model is that of a random walk on a regular lattice, where at each step the location jumps to another site according to some probability distribution. In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brownian Motion
Brownian motion, or pedesis (from grc, πήδησις "leaping"), is the random motion of particles suspended in a medium (a liquid or a gas). This pattern of motion typically consists of 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 and angular momenta remain null over time. The 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 internal energy (the equipartition theorem). This motion is named after the botanist Robert Brown, who first described the phenomenon in 1827, while looking t ... [...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 at hand sufficiently support a particular hypothesis. Hypothesis testing allows us to make probabilistic statements about population parameters. History Early use 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 . Modern origins and early controversy Modern significance testing is largely the product of Karl Pearson ( ''p''-value, Pearson's chi-squared test), William Sealy Gosset (Student's t-distribution), and Ronald Fisher ("null hypothesis", analysis of variance, " significance test"), while hypothesis testing was developed by Jerzy Neyman and Egon Pearson (son of Karl). Ronald Fisher began his life in statistics as a Bayesian (Zabell 1992), but Fisher soon grew disenchanted with ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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