The pair distribution function describes the distribution of distances between pairs of particles contained within a given volume. Mathematically, if a...

In statistical mechanics, the radial distribution function, (or pair correlation function) g ( r ) {\displaystyle g(r)} in a system of particles (atoms...

statistics, the cumulative distribution function (CDF) of a real-valued random variable X {\displaystyle X} , or just distribution function of X {\displaystyle...

Distributions, also known as Schwartz distributions are a kind of generalized function in mathematical analysis. Distributions make it possible to differentiate...

expressed in terms of a joint cumulative distribution function and either in terms of a joint probability density function (in the case of continuous variables)...

simulation techniques are most commonly used. The pair distribution function (or pair correlation function) of a material describes the probability of finding...

complementary data. Pair distribution function analysis can be performed on diffraction data to determine the probability of finding a pair of atoms separated...

The Wigner distribution function (WDF) is used in signal processing as a transform in time-frequency analysis. The WDF was first proposed in physics to...

mathematical analysis, the Dirac delta function (or δ distribution), also known as the unit impulse, is a generalized function on the real numbers, whose value...

quantile function of a distribution is the inverse of the cumulative distribution function. The quantile function of the standard normal distribution is called...

factors g i j {\displaystyle g_{ij}} , which is interpreted as the pair distribution function evaluated at the contact distance σ i j {\displaystyle \sigma...

hypergeometric function. For information on its inverse cumulative distribution function, see quantile function § Student's t-distribution. Certain values...

Ornstein and Frits Zernike in 1914. The connection to the density pair distribution function was given by the Ornstein–Zernike equation. The importance of...

system Pair distribution function Powder Diffraction File Probability density function Probability density function Probability distribution function (disambiguation)...

describes the homogeneity of density throughout an animal group. Pair distribution function – This parameter is usually used in physics to characterize the...

particles in linear flow fields, where the variable is given by the pair distribution function around a test particle. In the limit of low Péclet number, the...

In statistics, the Q-function is the tail distribution function of the standard normal distribution. In other words, Q ( x ) {\displaystyle Q(x)} is the...

[c,d]} . Finding the marginal cumulative distribution function from the joint cumulative distribution function is easy. Recall that: For discrete random...

test functions and distributions are topological vector spaces (TVSs) that are used in the definition and application of distributions. Test functions are...

distribution; another is the arctan function, which is related to the cumulative distribution function of a Cauchy distribution. A sigmoid function is...

correlation function in an elemental liquid or a solid (often called a Radial distribution function or a pair correlation function). Correlation functions between...

multiple variables is called a Dirichlet distribution. The probability density function (PDF) of the beta distribution, for 0 ≤ x ≤ 1 {\displaystyle 0\leq...

{1, 2, ..., K} into any other pair of non-singleton subsets. The characteristic function of the Dirichlet distribution is a confluent form of the Lauricella...

log_gamma function in Fortran 2008 and later. Some computing languages provide built-in functions to evaluate the Poisson distribution, namely R: function dpois(x...

crystalline materials with local disorder, can be examined using X-ray pair distribution function analysis, which requires high energy X-ray scattering data. By...

In mathematics, the error function (also called the Gauss error function), often denoted by erf, is a function e r f : C → C {\displaystyle \mathrm {erf}...

statistics, the multivariate normal distribution, multivariate Gaussian distribution, or joint normal distribution is a generalization of the one-dimensional...

many-particle systems. The HNC and PY integral equations provide the pair distribution functions of the particles in a classical fluid, even for very high coupling...

A hash function is any function that can be used to map data of arbitrary size to fixed-size values, though there are some hash functions that support...

partons (nonvalence partons) in addition to valence partons. A parton distribution function (PDF) within so called collinear factorization is defined as the...