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In statistical mechanics, the radial distribution function, (or pair correlation function) in a system of particles (atoms, molecules, colloids, etc.), describes how density varies as a function of distance from a reference particle. If a given particle is taken to be at the origin O, and if is the average number density of particles, then the ...
In mathematics a radial basis function (RBF) is a real-valued function whose value depends only on the distance between the input and some fixed point, either the origin, so that , or some other fixed point , called a center, so that . Any function that satisfies the property is a radial function. The distance is usually Euclidean distance ...
Cylindrical coordinate system. A cylindrical coordinate system with origin O, polar axis A, and longitudinal axis L. The dot is the point with radial distance ρ = 4, angular coordinate φ = 130°, and height z = 4. A cylindrical coordinate system is a three-dimensional coordinate system that specifies point positions by the distance from a ...
Rayleigh. In probability theory and statistics, the Rayleigh distribution is a continuous probability distribution for nonnegative-valued random variables. Up to rescaling, it coincides with the chi distribution with two degrees of freedom. The distribution is named after Lord Rayleigh (/ ˈreɪli /). [1]
Correlation function (astronomy) – Function describing the distribution of galaxies in the universe. Correlation function (statistical mechanics) – Measure of a system's order. Correlation function (quantum field theory) – Expectation value of time-ordered quantum operators. Mutual information – Measure of dependence between two variables.
Radial basis function kernel. In machine learning, the radial basis function kernel, or RBF kernel, is a popular kernel function used in various kernelized learning algorithms. In particular, it is commonly used in support vector machine classification. [1]
In statistical mechanics, the correlation function is a measure of the order in a system, as characterized by a mathematical correlation function. Correlation functions describe how microscopic variables, such as spin and density, at different positions are related. More specifically, correlation functions measure quantitatively the extent to ...
The cumulative distribution function of a real-valued random variable is the function given by [2]: p. 77. (Eq.1) where the right-hand side represents the probability that the random variable takes on a value less than or equal to . The probability that lies in the semi-closed interval , where , is therefore [2]: p. 84.