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Statistical characterization of distribution functions
In probability theory and statistics, the dispersion function is a functional that characterizes a probability distribution by measuring the expected
Dispersion_function
Complex complementary error function
permittivity from which dispersion relations are derived, hence it is sometimes referred to as the plasma dispersion function (although this name is sometimes
Faddeeva_function
Relation of wavelength/wavenumber as a function of a wave's frequency
a wave in the medium, as a function of frequency. In addition to the geometry-dependent and material-dependent dispersion relations, the overarching Kramers–Kronig
Dispersion_relation
Effect of a material on light
Dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency. Sometimes the term chromatic dispersion is used to refer to
Dispersion_(optics)
Statistical property quantifying how much a collection of data is spread out
In statistics, dispersion (also called variability, scatter, or spread) is the extent to which a distribution is stretched or squeezed. Common examples
Statistical_dispersion
Dispersion of waves on a water surface
In fluid dynamics, dispersion of water waves generally refers to frequency dispersion, which means that waves of different wavelengths travel at different
Dispersion_(water_waves)
Galaxy in the constellation Virgo
Diaferio, Antonaldo; Rines, Kenneth J. (April 2017). "The Velocity Dispersion Function of Very Massive Galaxy Clusters: Abell 2029 and Coma". The Astrophysical
IC_1101
Technique for amplifying ultrashort laser pulses
often described in dispersion orders: the group delay dispersion (GDD), third order of dispersion (TOD) etc. Figure 2 shows the dispersion orders for a grating
Chirped_pulse_amplification
Set of probability distributions
probability and statistics, the class of exponential dispersion models (EDM), also called exponential dispersion family (EDF), is a set of probability distributions
Exponential_dispersion_model
Mathematical relation assigning a probability event to a cost
optimization and decision theory, a loss function or cost function (sometimes also called an error function) is a function that maps an event or values of one
Loss_function
Mathematical simulation of how air pollutants disperse in the ambient atmosphere
Atmospheric dispersion modeling is the mathematical simulation of how air pollutants disperse in the ambient atmosphere. It is performed with computer
Atmospheric dispersion modeling
Atmospheric_dispersion_modeling
Multivalued function in mathematics
corrections to the dispersion relations of giant magnons, single spikes and GKP strings can be expressed in terms of the Lambert W function. In the t → ∞ limit
Lambert_W_function
Separation of a sound wave into component frequencies while passing through a material
In acoustics, acoustic dispersion is the phenomenon of a sound wave separating into its component frequencies as it passes through a material. The phase
Acoustic_dispersion
Summary statistic of variability
absolute deviation from any other fixed number. By using the general dispersion function, Habib (2011) defined MAD about median as D med = E [ | X − median
Average_absolute_deviation
Empirical law on the variance of species in a habitat
exponential dispersion models. Chapman & Hall. London Rayner, JMV (1985). "Linear relations in biomechanics: the statistics of scaling functions". Journal
Taylor's_law
Synchrotron located in India
high brightness. The lattice is a Double Bend Acromat with zero dispersion function along the long straight section. It has eight super periods each
Indus_2
Probability that random variable X is less than or equal to x
cumulative distribution function (CDF) of a real-valued random variable X {\displaystyle X} , or just distribution function of X {\displaystyle X} ,
Cumulative distribution function
Cumulative_distribution_function
In the physics of continuous media, spatial dispersion is a phenomenon where material parameters such as the permittivity or conductivity have dependence
Spatial_dispersion
Number of available physical states per energy unit
_{n}(k)} as a function of k to get the expression of Ω n ( E ) {\displaystyle \Omega _{n}(E)} as a function of the energy. If the dispersion relation is
Density_of_states
Physical phenomenon
frequency resonance condition. The set of resonances for a given dispersion function and the form of resonance conditions is partitioned into non-intersecting
Nonlinear_resonance
Function related to statistics and probability theory
A likelihood function (often simply called the likelihood) measures how well a statistical model explains observed data by calculating the probability
Likelihood_function
Short "burst" or "envelope" of restricted wave action that travels as a unit
equation, the wave packet's profile may remain constant (no dispersion) or it may change (dispersion) while propagating. Ideas related to wave packets – modulation
Wave_packet
Non-cryptographic hash function
Fowler–Noll–Vo (or FNV) is a non-cryptographic hash function created by Glenn Fowler, Landon Curt Noll, and Kiem-Phong Vo. The basis of the FNV hash algorithm
Fowler–Noll–Vo_hash_function
Smooth curve outlining the extremes of an oscillating signal
velocities both are c0. In so-called dispersive media the dispersion relation can be a complicated function of wavevector, and the phase and group velocities
Envelope_(waves)
Class of statistical models
variance function is proportional to the mean var ( Y i ) = τ μ i , {\displaystyle \operatorname {var} (Y_{i})=\tau \mu _{i},\,} where the dispersion parameter
Generalized_linear_model
Statistical data type
similar to others. Dispersion is measured and minimized in each group to maximize classification results. The dispersion function is used in information
Ordinal_data
materials change as a function of the wavelength of light used to measure them. This change as a function of wavelength is called the dispersion of the optical
Dispersion_staining
Family of probability distributions
representation uses the canonical parameter θ of an exponential dispersion model and cumulant function κ p ( θ ) = { α − 1 α ( θ α − 1 ) α , for p ≠ 1 , 2 − log
Tweedie_distribution
Electrokinetic potential in colloidal dispersions
potential is a scientific term for electrokinetic potential in colloidal dispersions. In the colloidal chemistry literature, it is usually denoted using the
Zeta_potential
Mathematical function for the probability a given outcome occurs in an experiment
measure of the dispersion of the distribution. Standard deviation: the square root of the variance, and hence another measure of dispersion. Symmetry: a
Probability_distribution
Dependence of group velocity on frequency
In optics, group-velocity dispersion (GVD) is a characteristic of a dispersive medium, used most often to determine how the medium affects the duration
Group-velocity_dispersion
Normalized measure of the dispersion of a probability distribution
probability theory and statistics, the index of dispersion, dispersion index, coefficient of dispersion, relative variance, or variance-to-mean ratio (VMR)
Index_of_dispersion
Number taken as representative of a list of numbers
tendency of a distribution is typically contrasted with its dispersion or variability; dispersion and central tendency are the often characterized properties
Average
Non-linear regression method
of the beta regression is linear in terms of the link function, but even in the equal dispersion case presented below, it is not a special case of generalised
Beta_regression
Measure of statistical dispersion
statistics, the interquartile range (IQR) is a measure of statistical dispersion, which is the spread of the data. The IQR may also be called the midspread
Interquartile_range
Wave on the surface of a fluid, dominated by surface tension
velocity, and there is no dispersion. At precisely this same wavelength, the phase velocity of gravity–capillary waves as a function of wavelength (or wave
Capillary_wave
Effective diffusion of a substance enhanced by shear flow, studied in fluid dynamics
Taylor dispersion or Taylor diffusion or Shear-induced dispersion is an apparent or effective diffusion of some scalar field arising on the large scale
Taylor_dispersion
Measure of the shape of a function
Moments of a function in mathematics are certain quantitative measures related to the shape of the function's graph. For example, if the function represents
Moment_(mathematics)
Measure of covariance of components of a random vector
statistics, a covariance matrix (also known as auto-covariance matrix, dispersion matrix, variance matrix, or variance–covariance matrix) is a square matrix
Covariance_matrix
Statistical measure of how far values spread from their average
In probability theory and statistics, variance is a measure of dispersion, meaning it is a measure of how far a set of numbers are spread out from their
Variance
Lens glass material with reduced refractive index shift with wavelength
Sigma Low Dispersion (LD): Tamron Super Low Dispersion (SD): Tokina Special Low Dispersion or Super Low Dispersion (SLD): Sigma Ultra-low Dispersion (UD):
Low-dispersion_glass
economics, price dispersion is variation in prices across sellers of the same item, holding fixed the item's characteristics. Price dispersion can be viewed
Price_dispersion
Material dispersion property
measure of a material's dispersion (change in refractive index as a function of wavelength), with high Vd values indicating low dispersion. It is named after
Abbe_number
Methods used in statistics
horizontal zero-axis with constant dispersion if the data follow a homogeneous Poisson process. Using Ripley's K function it can be determined whether points
Spatial descriptive statistics
Spatial_descriptive_statistics
Computational quantum mechanical modelling method to investigate electronic structure
treatment of systems which are dominated by dispersion (e.g. interacting noble gas atoms) or where dispersion competes significantly with other effects
Density_functional_theory
Method for measuring urban sprawl
Since the utilization density and dispersion are weighted with the weighting functions w 1 ( Dis ) {\displaystyle w_{1}({\text{Dis}})} and
Weighted_urban_proliferation
Covariance and correlation
processing, cross-correlation is a measure of similarity of two series as a function of the displacement of one relative to the other. This is also known as
Cross-correlation
Statistical measure
scale parameter, since its value determines the "scale" or statistical dispersion of the probability distribution. If s is large, then the distribution
Scale_parameter
be accomplished through a non-zero dispersion function for both beams of opposite sign at the IP. The dispersion is determined by the respective lattice
Monochromatization
Velocity at which the overall shape of a wave's amplitudes propagates
The phase velocity is: vp = ω/k. The function ω(k), which gives ω as a function of k, is known as the dispersion relation. If ω is directly proportional
Group_velocity
Relative measure of dispersion expressed as the ratio of standard deviation to the mean
and relative standard deviation (RSD), is a standardized measure of dispersion of a probability distribution or frequency distribution. It is defined
Coefficient_of_variation
Interactions between groups of atoms that do not arise from chemical bonds
der Waals forces are usually described as a combination of the London dispersion forces between "instantaneously induced dipoles", Debye forces between
Van_der_Waals_force
Galaxy cluster in the constellation Pisces
with a big velocity dispersion of σ > 160 km s−1 and much steeper as expected, when researchers created a velocity dispersion function of Dn4000 > 1.5 within
Abell_68
American physicist and professor (1942–2019)
Summers, Danny; Thorne, Richard M. (1991). "The modified plasma dispersion function". Physics of Fluids B: Plasma Physics. 3 (8): 1835–1847. Bibcode:1991PhFlB
Richard_M._Thorne
Dispersion of Jews around the globe
The Jewish diaspora (Hebrew: גוֹלָה gōlā), alternatively the dispersion (תְּפוּצָה təfūṣā) or the exile (גָּלוּת gālūṯ; Yiddish: גלות gōləs), consists
Jewish_diaspora
Type of average of a collection of numbers
0° (or 360°) is geometrically a better average value: there is lower dispersion about it (the points are both 1° from it and 179° from 180°, the putative
Arithmetic_mean
Probability of survival beyond any specified time
certain time. The survival function is also known as the survivor function or reliability function. The term reliability function is common in engineering
Survival_function
independent variable interquartile range (IQR) A measure of the statistical dispersion or spread of a dataset, defined as the difference between the 25th and
Glossary of probability and statistics
Glossary_of_probability_and_statistics
out to be the dispersion relation for the linear waves, and the averaged Lagrangian for linear waves is always the dispersion function G ( ω , k ) {\displaystyle
Averaged_Lagrangian
Mixture of an insoluble substance microscopically dispersed throughout another substance
colloidal emulsions, colloidal suspensions, colloidal foams, colloidal dispersions, or hydrosols. Colloidal silica gel with light opalescence A dollop of
Colloid
Fundamental theorem in probability theory and statistics
doi:10.1080/00029890.1995.12004608. Jørgensen, Bent (1997). The Theory of Dispersion Models. Chapman & Hall. ISBN 978-0412997112. Bárány, Imre; Vu, Van (2007)
Central_limit_theorem
Sequence of data points over time
entropy Sample entropy Fourier entropy [uk] Wavelet entropy Dispersion entropy Fluctuation dispersion entropy Rényi entropy Higher-order methods Marginal predictability
Time_series
Empirical relationship between refractive index and wavelength
particular transparent medium. The equation is used to determine the dispersion of light in the medium. It was first proposed in 1872 by Wolfgang Sellmeier
Sellmeier_equation
Statistical measure of variability
data is 1. The median absolute deviation is a measure of statistical dispersion. Moreover, the MAD is a robust statistic, being more resilient to outliers
Median_absolute_deviation
Relaxation model
Curie–von Schweidler law Cole, Kenneth Stewart; Cole, Robert Hugh (1941). "Dispersion and Absorption in Dielectrics I. Alternating Current Characteristics"
Cole–Cole_equation
Frequency swept signal
transmission systems, interacts with the dispersion properties of the materials, increasing or decreasing total pulse dispersion as the signal propagates. The name
Chirp
Effect in accelerator physics
function and its derivative, respectively η h , v {\displaystyle \eta _{h,v}} and η h , v ′ {\displaystyle \eta '_{h,v}} is the dispersion function and
Intrabeam_scattering
Correlation of a signal with a time-shifted copy of itself, as a function of shift
Pearson correlation between values of the process at different times, as a function of the two times or of the time lag. Let { X t } {\displaystyle \left\{X_{t}\right\}}
Autocorrelation
Type of statistics
data set are measures of central tendency and measures of variability or dispersion. Measures of central tendency include the mean, median and mode, while
Descriptive_statistics
Middle quantile of a data set or probability distribution
deviation. For practical purposes, different measures of location and dispersion are often compared on the basis of how well the corresponding population
Median
Set of statistical processes for estimating the relationships among variables
regression models propose that Y i {\displaystyle Y_{i}} is a function (regression function) of X i {\displaystyle X_{i}} and β {\displaystyle \beta }
Regression_analysis
Variable representing a random phenomenon
refers to neither randomness nor variability but instead is a mathematical function in which the domain is the set of possible outcomes in a sample space (e
Random_variable
Data visualization
The spacings in each subsection of the box plot indicate the degree of dispersion (spread) and skewness of the data, which are usually described using the
Box_plot
Probability distribution
real-valued random variable. The general form of its probability density function is f ( x ) = 1 2 π σ 2 exp ( − ( x − μ ) 2 2 σ 2 ) . {\displaystyle f(x)={\frac
Normal_distribution
Stable dispersion of polymer microparticles in an aqueous medium
Latex (pl. latices) is an emulsion (stable dispersion) of polymer microparticles in water. Latices are found in nature, but synthetic latices are common
Latex
Probability distribution
distribution, s is the dispersion, ƒ is the family parameter, I is the indicator function, Φ is the cumulative distribution function of the standard normal
Box–Cox_distribution
Measure for evaluating probabilistic forecasts
In decision theory, both a scoring rule as well as a scoring function provide an ex post summary measure for the evaluation of the quality of a prediction
Scoring_rule
Species of slug
centimeters (9.8 in) long. An important function of this particular species is the role it plays in seed dispersion. Ariolimax columbianus is endemic to
Ariolimax_columbianus
Theory in optics
1982. The generalized mathematical description of multiple-prism dispersion, as a function of the angle of incidence, prism geometry, prism refractive index
Multiple-prism dispersion theory
Multiple-prism_dispersion_theory
Property in optics
"normal dispersion", in contrast to "anomalous dispersion", where the refractive index increases with wavelength. For visible light normal dispersion means
Refractive_index
Quantum anomaly
A Kohn anomaly or the Kohn effect is an anomaly in the dispersion relation of a phonon branch in a metal. The anomaly is named for Walter Kohn, who first
Kohn_anomaly
Distribution function associated with the empirical measure of a sample
an empirical distribution function (a.k.a. an empirical cumulative distribution function, eCDF) is the distribution function associated with the empirical
Empirical distribution function
Empirical_distribution_function
Type of statistics
deviation and interquartile range are robust measures of statistical dispersion, while the standard deviation and range are not. Trimmed estimators and
Robust_statistics
Statistical test comparing two probability distributions
distribution function of the sample and the cumulative distribution function of the reference distribution, or between the empirical distribution functions of two
Kolmogorov–Smirnov_test
Atmospheric dispersion models are computer programs that use mathematical algorithms to simulate how pollutants in the ambient atmosphere disperse and
List of atmospheric dispersion models
List_of_atmospheric_dispersion_models
Mathematical transform that expresses a function of time as a function of frequency
takes a function as input and outputs another function that describes the extent to which various frequencies are present in the original function. The output
Fourier_transform
Measure of the error of an estimator
difference between the estimated values and the true value. MSE is a risk function, corresponding to the expected value of the squared error loss. The fact
Mean_squared_error
Method used in statistics, pattern recognition, and other fields
discriminant analysis (NDA), canonical variates analysis (CVA), or discriminant function analysis is a generalization of Fisher's linear discriminant, a method
Linear_discriminant_analysis
Value that appears most often in a set of data
random variable, the mode is the value x at which the probability mass function P(X) takes its maximum value, i.e., x = argmaxxi P(X = xi). In other words
Mode_(statistics)
Measure of linear correlation
cross-product of standardized variables Function of the angle between two standardized regression lines Function of the angle between two variable vectors
Pearson correlation coefficient
Pearson_correlation_coefficient
Reactor simulation model
transport by diffusion or dispersion. L {\displaystyle L} = characteristic length (m) D L {\displaystyle D_{L}} = effective dispersion coefficient ( m2/s) U
Plug_flow_reactor_model
modeling), polynomial functions and rational functions are sometimes used as an empirical technique for curve fitting. A polynomial function is one that has
Polynomial and rational function modeling
Polynomial_and_rational_function_modeling
Type of statistical measure over subsets of a dataset
viewed as a low-pass finite impulse response filter. Because the boxcar function outlines its filter coefficients, it is called a boxcar filter. It is sometimes
Moving_average
Distinction between nominal, ordinal, interval and ratio variables
mode is also allowed, but not the mean), and the appropriate measure of dispersion is percentile or quartile (the standard deviation is not allowed). Those
Level_of_measurement
Measure of the asymmetry of random variables
{Q(3/4)-Q(1/4)}{2}}} , which for symmetric distributions is equal to the MAD measure of dispersion.[citation needed] Other names for this measure are Galton's measure of
Skewness
Relationship of a signal transducer
Green–Kubo relations Fluctuation theorem Dispersion (optics) Lindbladian Semilinear response Green's function Impulse response Resolvent formalism Propagator
Linear_response_function
Electrically insulating substance able to be polarised by an applied electric field
permittivity of the dielectric is a complex function of the frequency of the electric field. Dielectric dispersion is very important for the applications of
Dielectric
Statistic measuring inter-rater agreement for categorical items
Generalized/power Geometric Harmonic Heronian Heinz Lehmer Median Mode Dispersion Average absolute deviation Coefficient of variation Interquartile range
Cohen's_kappa
Branch of physics that studies light
medium is said to have positive dispersion or normal dispersion. If D is greater than zero, the medium has negative dispersion. If a light pulse is propagated
Optics
Pulse that is substantially slowed to less than the speed of light
dispersion, i.e., peaks in the dispersion relation. Schemes are generally grouped into two categories: material dispersion and waveguide dispersion.
Slow_light
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