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In probability theory, random element is a generalization of the concept of random variable to more complicated spaces than the simple real line. The concept was introduced by Maurice Fréchet () who commented that the “development of probability theory and expansion of area of its applications have led to necessity to pass from schemes where (random) outcomes of experiments can be described ...
In probability theory, a random measure is a measure-valued random element. [ 1 ] [ 2 ] Random measures are for example used in the theory of random processes , where they form many important point processes such as Poisson point processes and Cox processes .
Sometimes a random variable is taken to be automatically valued in the real numbers, with more general random quantities instead being called random elements. According to George Mackey , Pafnuty Chebyshev was the first person "to think systematically in terms of random variables".
Chemical nomenclature, replete as it is with compounds with very complex names, is a repository for some names that may be considered unusual. A browse through the Physical Constants of Organic Compounds in the CRC Handbook of Chemistry and Physics (a fundamental resource) will reveal not just the whimsical work of chemists, but the sometimes peculiar compound names that occur as the ...
A random process is a sequence of random variables whose outcomes do not follow a deterministic pattern, but follow an evolution described by probability distributions. These and other constructs are extremely useful in probability theory and the various applications of randomness .
This leads to tensor-valued random fields [clarification needed] in which the key role is played by a statistical volume element (SVE), which is a spatial box over which properties can be averaged; when the SVE becomes sufficiently large, its properties become deterministic and one recovers the representative volume element (RVE) of ...
“There’s just a random element, and often seasonal flu is quite bad,” he told The Independent. “It’s looking quite similar to the flu season last year, and it could be that this ends up ...
Where those random numbers fail to be actually random, any subsequent statistical analysis may suffer from systematic bias. Elements of statistical practice that depend on randomness include: choosing a representative sample of the population being examined, disguising the protocol of a study from a participant (see randomized controlled trial ...