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Distribution of distances between pairs of particles in a given volume
The pair distribution function describes the distribution of distances between pairs of particles contained within a given volume. Mathematically, if a
Pair_distribution_function
Probability that random variable X is less than or equal to x
statistics, the cumulative distribution function (CDF) of a real-valued random variable X {\displaystyle X} , or just distribution function of X {\displaystyle
Cumulative distribution function
Cumulative_distribution_function
Description of particle density in statistical mechanics
In statistical mechanics, the radial distribution function, (or pair correlation function) g ( r ) {\displaystyle g(r)} in a system of particles (atoms
Radial_distribution_function
Atomic-scale non-crystalline structure of liquids and glasses
simulation techniques are most commonly used. The pair distribution function (or pair correlation function) of a material describes the probability of finding
Structure of liquids and glasses
Structure_of_liquids_and_glasses
Statistical mechanics framework
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
Chapman–Enskog_theory
Non-crystalline solid
complementary data. Pair distribution function analysis can be performed on diffraction data to determine the probability of finding a pair of atoms separated
Amorphous_solid
Part of signal processing in time-frequency analysis
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
Wigner_distribution_function
Type of probability distribution
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)
Joint probability distribution
Joint_probability_distribution
Topological vector spaces
test functions and distributions are topological vector spaces (TVSs) that are used in the definition and application of distributions. Test functions are
Spaces of test functions and distributions
Spaces_of_test_functions_and_distributions
Probability distribution
hypergeometric function. For information on its inverse cumulative distribution function, see quantile function § Student's t-distribution. Certain values
Student's_t-distribution
Generalized function whose value is zero everywhere except at zero
Dirac delta function (or δ {\displaystyle {\boldsymbol {\delta }}} distribution), also known as the unit impulse, is a generalized function on the real
Dirac_delta_function
Approximation in mathematics
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
Method of matched asymptotic expansions
Method_of_matched_asymptotic_expansions
Statistical modeling method
on the current configuration. Commonly used data include the pair distribution function and its Fourier transform, the latter of which is derived directly
Reverse_Monte_Carlo
Probability distribution
quantile function of a distribution is the inverse of the cumulative distribution function. The quantile function of the standard normal distribution is called
Normal_distribution
Topics referred to by the same term
system Powder Diffraction File Pair distribution function Probability density function Probability distribution function (disambiguation) Parkinson's Disease
PDF_(disambiguation)
Statistics function
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
Q-function
Synchrotron radiation facility at Lund University in Sweden
research began in 1987. The ring had 8 dipole bending magnets ordered in 4 pairs called double bend achromats, DBA. It had a circumference of 32 metres,
MAX_IV_Laboratory
Probability distribution
{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
Dirichlet_distribution
In biology, any group of fish that stay together for social reasons
describes the homogeneity of density throughout an animal group. Pair distribution function – This parameter is usually used in physics to characterize the
Shoaling_and_schooling
Computational quantum mechanical modelling method to investigate electronic structure
Ornstein and Frits Zernike in 1914. The connection to the density pair distribution function was given by the Ornstein–Zernike equation. The importance of
Density_functional_theory
Mathematical function having a characteristic S-shaped curve or sigmoid curve
tangent functions have been used as the activation function of artificial neurons. Sigmoid curves are also common in statistics as cumulative distribution functions
Sigmoid_function
Discrete probability distribution
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
Poisson_distribution
Aspect of probability and statistics
[c,d]} . Finding the marginal cumulative distribution function from the joint cumulative distribution function is easy. Recall that: For discrete random
Marginal_distribution
Measure of a system's order
correlation function in an elemental liquid or a solid (often called a Radial distribution function or a pair correlation function). Correlation functions between
Correlation function (statistical mechanics)
Correlation_function_(statistical_mechanics)
Objects that generalize functions
Distributions (or generalized functions) are objects that generalize the classical notion of functions in mathematical analysis. Distributions make it
Distribution (mathematical analysis)
Distribution_(mathematical_analysis)
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
Classical-map hypernetted-chain method
Classical-map_hypernetted-chain_method
Particle accelerator designed to produce intense x-ray beams
crystalline materials with local disorder, can be examined using X-ray pair distribution function analysis, which requires high energy X-ray scattering data. By
Synchrotron_light_source
Probability distribution
multiple variables is called a Dirichlet distribution. The probability density function (PDF) of the beta distribution, for 0 ≤ x ≤ 1 {\displaystyle 0\leq
Beta_distribution
Mathematical conjecture
which, as Freeman Dyson pointed out to him, is the same as the pair correlation function of random Hermitian matrices. Under the assumption that the Riemann
Montgomery's pair correlation conjecture
Montgomery's_pair_correlation_conjecture
Generalization of the one-dimensional normal distribution to higher dimensions
statistics, the multivariate normal distribution, multivariate Gaussian distribution, or joint normal distribution is a generalization of the one-dimensional
Multivariate normal distribution
Multivariate_normal_distribution
Wigner distribution function in physics as opposed to in signal processing
The Wigner quasiprobability distribution, also called the Wigner function or the Wigner–Ville distribution, after Eugene Wigner and Jean-André Ville, is
Wigner quasiprobability distribution
Wigner_quasiprobability_distribution
Model of hadrons
partons (nonvalence partons) in addition to valence partons. A parton distribution function (PDF) within so called collinear factorization is defined as the
Parton_(particle_physics)
Solution theory
information. The radial distribution function (RDF), also termed the pair distribution function or the pair correlation function, is a measure of local
Kirkwood–Buff_solution_theory
Statistical hypothesis test
"Student's t-Distribution". mathworld.wolfram.com. David, H. A.; Gunnink, Jason L. (1997). "The Paired t Test Under Artificial Pairing". The American
Student's_t-test
Experimental method in X-ray diffraction
diffraction Materials science Metallurgy Neutron diffraction Pair distribution function Solid state chemistry Texture (crystalline) Ultrafast x-ray X-ray
Powder_diffraction
{\displaystyle g_{\rm {indirect}}(r)} is the radial distribution function without the direct interaction between pairs u ( r ) {\displaystyle u(r)} included; i.e
Percus–Yevick_approximation
National laboratory in New York, United States
development) 27-ID: High Energy X-ray Diffraction (HEX) 28-ID-1: Pair Distribution Function (PDF) 28-ID-2: X-Ray Powder Diffraction (XPD) 6-BM: Beamline for
National Synchrotron Light Source II
National_Synchrotron_Light_Source_II
Family of probability distributions
implies that the variance function obeys the relationship V(μ) = μp. The unit deviance of a reproductive Tweedie distribution is given by d ( y , μ ) =
Tweedie_distribution
Mathematical transform that expresses a function of time as a function of frequency
function, of substantial importance in probability theory and statistics as well as in the study of physical phenomena exhibiting normal distribution
Fourier_transform
Iron oxyhydroxide mineral
hydromaghemite has been proposed by Michel et al., in 2007–2010, based on pair distribution function (PDF) analysis of x-ray total scattering data. The structural
Ferrihydrite
Sigmoid shape special function
mathematics, the error function (also called the Gauss error function), often denoted by e r f {\displaystyle \mathbf {erf} } , is the function erf ( z ) = 2
Error_function
Cathode material for lithium batteries
Torbjörn; Edström, Kristina; Brant, William R. (2019-07-23). "Neutron Pair Distribution Function Study of FePO 4 and LiFePO 4". Chemistry of Materials. 31 (14):
Lithium_iron_phosphate
German material scientist (born 1958)
(2002). Structure of V2O5⊙ n H2O Xerogel Solved by the Atomic Pair Distribution Function Technique. Journal of the American Chemical Society, 124(34),
Thomas_Vogt
Ability of a substance to exist in more than one distinct amorphous state
structure of liquids and glasses polymorphism (materials science) Pair distribution function Mishima, O.; Mishima, Osamu (1998). "The relationship between
Polyamorphism
Probability distribution with more than one mode
probability density function, as shown in Figures 1 and 2. Categorical, continuous, and discrete data can all form multimodal distributions. Among univariate
Multimodal_distribution
Probability of shared birthdays
average number of people required to find a pair with the same birthday. If we consider the probability function Pr[n people have at least one shared birthday]
Birthday_problem
Polymer of carbon monoxide (CO)
Investigations of Liquid and Polymerized CO up to 20 GPa Using Pair Distribution Function Analysis" (PDF). Retrieved 30 May 2013. Bernard, Stephane (Feb
Polycarbonyl
liquid, amorphous and nanocrystalline materials as well as for pair distribution function analysis. Realization of the Materials oscilloscope. Simple diffraction
High-energy_X-rays
French environmental mineralogist and biogeochemist
neutron diffraction pattern, and in 2014 by simulation of the pair distribution function measured by high-energy X-ray scattering. In 1997, he and Victor
Alain_Manceau
Statistical distribution for dependence between random variables
a copula is a multivariate cumulative distribution function for which the marginal probability distribution of each variable is uniform on the interval [0
Copula_(statistics)
Padre Bancalari Painlevé paradox Pair-instability supernova Pair annihilation Pair distribution function Pair potential Pair production Pake doublet Pakistan
Index_of_physics_articles_(P)
Mapping arbitrary data to fixed-size values
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
Hash_function
Clarendon Press: Oxford (2000). Van Hove, L.; McVoy, K.W. (1962). "Pair distribution functions and scattering phenomena". Nuclear Physics. 33. Elsevier BV:
Quasielastic neutron scattering
Quasielastic_neutron_scattering
Continuous function that is not absolutely continuous
endpoints described above. The Cantor function can also be seen as the cumulative probability distribution function of the 1/2-1/2 Bernoulli measure μ supported
Cantor_function
Iron nickel sulfide mineral
order and crystallite size of the initial FeS precipitate from pair distribution function analysis". Chemistry of Materials. 17 (25): 6246–6255. doi:10
Mackinawite
Continuous probability distribution for a non-negative random variable
in shape to the log-normal distribution but has heavier tails . Unlike the log-normal, its cumulative distribution function can be written in closed form
Log-logistic_distribution
Functions in mathematics
holomorphic function yield harmonic functions on R 2 {\displaystyle \mathbb {R} ^{2}} (these are said to be a pair of harmonic conjugate functions). Conversely
Harmonic_function
Early block substitution cipher
the name of Lord Playfair for promoting its use. The technique encrypts pairs of letters (bigrams or digrams), instead of single letters as in the simple
Playfair_cipher
Animal cognition
describes the homogeneity of density throughout an animal group. Pair Distribution Function: This parameter is usually used in physics to characterize the
Collective_animal_behavior
Function returning minus 1, zero or plus 1
In mathematics, the sign function or signum function (from signum, Latin for "sign") is a function that has the value −1, +1 or 0 according to whether
Sign_function
Concept in condensed matter physics
properties of even the interacting electron gas, including the pair-distribution functions at finite T {\displaystyle T} , has been given using the classical
Thomas–Fermi_screening
Probability distribution
product distribution is a probability distribution constructed as the distribution of the product of random variables having two other known distributions. Given
Distribution of the product of two random variables
Distribution_of_the_product_of_two_random_variables
Association of one output to each input
function is uniquely represented by the set of all pairs (x, f (x)), called the graph of the function, a popular means of illustrating the function.
Function_(mathematics)
Integral of the Gaussian function, equal to sqrt(π)
normal distribution. The same integral with finite limits is closely related to both the error function and the cumulative distribution function of the
Gaussian_integral
Analytic function in mathematics
The Riemann zeta function or Euler–Riemann zeta function, denoted by the lowercase Greek letter ζ (zeta), is a mathematical function of a complex variable
Riemann_zeta_function
Method of solution to differential equations
Green's functions are not necessarily functions of a real variable but are generally understood in the sense of distributions. Green's functions are also
Green's_function
Variable representing a random phenomenon
random variable and its distribution is a discrete probability distribution, i.e. can be described by a probability mass function that assigns a probability
Random_variable
Order-preserving mathematical function
In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept
Monotonic_function
Measure of inequality of a statistical distribution
a quadratic function across pairs of intervals or building an appropriately smooth approximation to the underlying distribution function that matches
Gini_coefficient
Statistical hypothesis test
normal distribution of the differences between paired individuals cannot be assumed. Instead, it assumes a weaker hypothesis that the distribution of this
Wilcoxon_signed-rank_test
Real function with secant line between points above the graph itself
function is called convex if the line segment between any two distinct points on the graph of the function lies above or on the graph of the function
Convex_function
Function used in signal processing
processing and statistics, a window function (also known as an apodization function or tapering function) is a mathematical function that is zero-valued outside
Window_function
93.1430. ISSN 0031-899X. Van Hove, L.; McVoy, K.W. (1962). "Pair distribution functions and scattering phenomena". Nuclear Physics. 33. Elsevier BV:
Quasielastic_scattering
Measure of linear correlation
freedom are reduced. For data that follow a bivariate normal distribution, the exact density function f(r) for the sample correlation coefficient r of a normal
Pearson correlation coefficient
Pearson_correlation_coefficient
Mathematical function, inverse of an exponential function
contained the common logarithms of trigonometric functions. Another critical application was the slide rule, a pair of logarithmically divided scales used for
Logarithm
Australian-American physicist
structure of nanomaterials from experimental data, particularly pair distribution function (PDF) analysis. A 2006 paper described general strategies for
Phillip_Duxbury
Method for structure analysis of biological materials
provide the Fourier transform of the histogram of atomic pair distances (pair distribution function) for a given protein. This can serve as a structural constraint
Biological small-angle scattering
Biological_small-angle_scattering
Probability distribution on the circle
Mises distribution is a special case of the von Mises–Fisher distribution on the N-dimensional sphere. The von Mises probability density function for the
Von_Mises_distribution
Conjecture on zeros of the zeta function
the distribution of the zeros of the zeta function on the critical line. One conjectural picture is that the critical zeros of the zeta function behave
Riemann_hypothesis
Theorem
{D}}} arises by pairing the image distribution with a test function. A simple example is that the natural embedding of the test function space D {\displaystyle
Schwartz_kernel_theorem
Distance function defined between probability distributions
distance or Kantorovich–Rubinstein metric is a distance function defined between probability distributions on a given metric space M {\displaystyle M} . It is
Wasserstein_metric
Diagnostic plot of binary classifier ability
ROC curve is obtained as the cumulative distribution function (CDF, area under the probability distribution from − ∞ {\displaystyle -\infty } to the
Receiver operating characteristic
Receiver_operating_characteristic
Type of statistical analysis
drawn from a given parametric family of probability distributions. Statistics defined to be a function on a sample, without dependency on a parameter. An
Nonparametric_statistics
Type of cryptographic attack
Such a pair x 1 , x 2 {\displaystyle x_{1},x_{2}} is called a collision. The method used to find a collision is simply to evaluate the function f {\displaystyle
Birthday_attack
Function that is discontinuous at rationals and continuous at irrationals
distributed similarly to Thomae's function. If pairs of positive integers m , n {\displaystyle m,n} are sampled from a distribution f ( n , m ) {\displaystyle
Thomae's_function
Function describing the distribution of galaxies in the universe
correlation function describes the distribution of objects (often stars or galaxies) in the universe. By default, "correlation function" refers to the
Correlation function (astronomy)
Correlation_function_(astronomy)
Tent function, often used in signal processing
A triangular function (also known as a triangle function, hat function, or tent function) is a function whose graph takes the shape of a triangle. Often
Triangular_function
Simple encryption method
are 26 letters in the basic Latin alphabet and 26 = 2 × 13, the ROT13 function is its own inverse: ROT 13 ( ROT 13 ( x ) ) = x {\displaystyle
ROT13
Diagram that shows all possible logical relations between a collection of sets
Probability distribution Bernoulli distribution Binomial distribution Exponential distribution Normal distribution Pareto distribution Poisson distribution Probability
Venn_diagram
Fourth standardized moment in statistics
better generalizes to multivariate distributions, especially when independence is not assumed. The cokurtosis between pairs of variables is an order four tensor
Kurtosis
Comparison of two distributions
probability distribution functions F and G, with associated quantile functions F−1 and G−1 (the inverse function of the CDF is the quantile function), the Q–Q
Q–Q_plot
Generalization of the binomial distribution
given extraction will be in color i. The probability mass function of this multinomial distribution is: f ( x 1 , … , x k ; n , p 1 , … , p k ) = Pr ( X 1
Multinomial_distribution
Monte Carlo algorithm
density, proposal function, or jumping distribution. A common choice for g ( x ∣ y ) {\displaystyle g(x\mid y)} is a Gaussian distribution centered at y {\displaystyle
Metropolis–Hastings_algorithm
Statistical transform
1), too. The latter can be seen by calculating the cumulative distribution function for s in the interval (0, 1). This is the area of a circle with
Box–Muller_transform
Response if an optical system to a point source of light
The point spread function (PSF) describes the response of a focused optical imaging system to an idealized point source of light. In casual terms, for
Point_spread_function
Construction for adding objects to a Hilbert space
The latter, dual to Φ in its 'test function' topology, is realised as a space of distributions or generalised functions of some sort, and the linear functionals
Rigged_Hilbert_space
Statistical hypothesis test
observations of the pairs. Chi-squared tests often refers to tests for which the distribution of the test statistic approaches the χ2 distribution asymptotically
Chi-squared_test
Statistical model
those (infinitely many) random variables, and as such, it is a distribution over functions with a continuous domain, e.g. time or space. The concept of
Gaussian_process
Mathematical description of quantum state
measurements, to the wave function ψ and calculate the statistical distributions for measurable quantities. Wave functions can be functions of variables other
Wave_function
Family of probability distributions often used to model tails or extreme values
parameterization was introduced by James Pickands III . The cumulative distribution function of X ∼ GPD ( μ , σ , ξ ) {\displaystyle X\sim {\text{GPD}}(\mu
Generalized Pareto distribution
Generalized_Pareto_distribution
PAIR DISTRIBUTION-FUNCTION
PAIR DISTRIBUTION-FUNCTION
Boy/Male
Muslim/Islamic
Divider distributor
Male
English
 Anglicized form of Hebrew Yaiyr, JAIR means "whom God enlightens." In the bible, this is the name of several characters, including a descendant of Manasseh. Anglicized form of Hebrew Yauwr, meaning "forested." In the bible, this is the name of the father of Elhanan.
Girl/Female
Arabic
Distributor
Boy/Male
Muslim
Distributor, Divider
Female
Persian/Iranian
(پری) Persian name PARI means "fairy."
Female
Welsh
Welsh form of Greek Maria, MAIR means "obstinacy, rebelliousness" or "their rebellion."
Boy/Male
Muslim
Mountain range
Surname or Lastname
Scottish spelling of Irish Hare.English
Scottish spelling of Irish Hare.English : nickname for someone with some peculiarity of the hair, from Middle English here ‘hair’.
Boy/Male
Muslim
Distributor, Divider
Surname or Lastname
English
English : nickname meaning ‘handsome’, ‘beautiful’, ‘fair’, Middle English fair, fayr, Old English fæger. The word was also occasionally used as a personal name in Middle English, applied to both men and women.Irish : translation of Gaelic fionn ‘fair’, which Woulfe describes as ‘a descriptive epithet that supplanted the real surname’, or a reduced Anglicized form of Gaelic Mac F(h)inn, a variant of Mag Fhinn (see McGinn).
Male
Hebrew
(×™Ö¸×ִיר) Variant spelling of Hebrew Yaiyr, YAIR means "whom God enlightens."Â
Girl/Female
Indian, Sikh
Distributing Happiness
Surname or Lastname
English and Irish
English and Irish : variant spelling of Fair.
Surname or Lastname
English
English : habitational name from Parr in Lancashire, which was named in Old English with pearr ‘enclosure’.German : from Middle Low German parre ‘parish’, ‘district’, ‘minister’s house’; a metonymic occupational name for a parson or for someone who worked in a parsonage or manse. Compare Pfarr.
Boy/Male
Arabic, British, Islamic, Malaysian, Muslim, Pakistani, Tamil, Urdu
Distribution
Boy/Male
Indian
Distributor, Divider
Boy/Male
Hindu
Brave
Boy/Male
Muslim
Walking, Going on foot
Male
English
Variant spelling of English Gare, GAIR means "spear."
Boy/Male
Indian
Distributor, Divider
PAIR DISTRIBUTION-FUNCTION
PAIR DISTRIBUTION-FUNCTION
Male
Hebrew
(מְתוּש×Ö¸×ֵל) Hebrew name METHUWSHAEL means "man of God." In the bible, this is the name of a descendant of Cain.
Boy/Male
Arabic, Hindu, Indian, Muslim
Shining
Surname or Lastname
English (Suffolk)
English (Suffolk) : probably a variant of Norfolk.
Girl/Female
Muslim
Fragrant
Boy/Male
Arabic
Brave
Male
Celtic
, high king; king paramount.
Boy/Male
Arabic, Indian, Kannada, Muslim
Nobility; Excellence
Boy/Male
Irish
Dark. Many Irish and Scottish names have the meaning 'dark' or 'black.
Boy/Male
Tamil
Vardhaman | வரà¯à®¤à®®à®¾à®¨
Lord Mahavir
Girl/Female
Indian
Clear, Pure, Most beautiful one
PAIR DISTRIBUTION-FUNCTION
PAIR DISTRIBUTION-FUNCTION
PAIR DISTRIBUTION-FUNCTION
PAIR DISTRIBUTION-FUNCTION
PAIR DISTRIBUTION-FUNCTION
v. i.
Same as To pair off. See phrase below.
n.
Hair (human or animal) used for various purposes; as, hair for stuffing cushions.
a.
Expressing separation; denoting a taking singly, not collectively; as, a distributive adjective or pronoun, such as each, either, every; a distributive numeral, as (Latin) bini (two by two).
v. t.
To unite in couples; to form a pair of; to bring together, as things which belong together, or which complement, or are adapted to one another.
n.
Two of a sort; a span; a yoke; a couple; a brace; as, a pair of horses; a pair of oxen.
n.
See Parr.
v. i.
To make distribution.
pl.
of Pair
a.
Having fair or light-colored hair.
n.
The act of distributing or dispensing; the act of dividing or apportioning among several or many; apportionment; as, the distribution of an estate among heirs or children.
n.
Distribution; apportionment.
n.
Disposition; distribution; management.
n.
Two things of a kind, similar in form, suited to each other, and intended to be used together; as, a pair of gloves or stockings; a pair of shoes.
n.
A distributive adjective or pronoun; also, a distributive numeral.
n.
A number of things resembling one another, or belonging together; a set; as, a pair or flight of stairs. "A pair of beads." Chaucer. Beau. & Fl. "Four pair of stairs." Macaulay. [Now mostly or quite disused, except as to stairs.]
v. t.
To make fair or beautiful.
n.
Distribution; dealing; apportionment.
adv.
By distribution; singly; not collectively; in a distributive manner.
n.
A single thing, composed of two pieces fitted to each other and used together; as, a pair of scissors; a pair of tongs; a pair of bellows.
a.
Of or pertaining to distribution.