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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
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)
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
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
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
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)
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Statistical value representing the center or average of a distribution
tendency of a distribution is typically contrasted with its dispersion or variability; dispersion and central tendency are the often characterized properties
Central_tendency
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
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
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
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
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
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
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
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
Effective diffusion of a substance enhanced by shear flow, studied in fluid dynamics
{w}}=a{\mathit {Pe}}} . Dispersion is also a function of channel geometry. An interesting phenomenon for example is that the dispersion of a flow between two
Taylor_dispersion
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
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
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
In the physics of continuous media, spatial dispersion is a phenomenon where material parameters such as the permittivity or conductivity have dependence
Spatial_dispersion
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
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
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
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
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
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
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
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
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
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
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
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
Numeric quantity representing the center of a collection of numbers
geometric mean Weighted harmonic mean Mathematics portal Statistical dispersion Central tendency Median Mode Descriptive statistics Kurtosis Law of averages
Mean
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
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
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
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
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
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
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
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
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
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
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
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
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
Statistical model for a binary dependent variable
the value "1"), hence the labeling; the function that converts log-odds to probability is the logistic function, hence the name. The unit of measurement
Logistic_regression
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
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
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
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
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
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
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
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
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
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
Dynamic disturbance in a medium or field
non-dispersive. In case of other forms of the dispersion relation, we have dispersive waves. The dispersion relationship depends on the medium through which
Wave
Function of the observed sample results
for instance using Fisher's combined probability test. The p-value is a function of the chosen test statistic T {\displaystyle T} and is therefore a random
P-value
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)
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
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
Statistical modeling method
of the explanatory variables (or predictors) is assumed to be an affine function of those values; less commonly, the conditional median or some other quantile
Linear_regression
Method of estimating the parameters of a statistical model, given observations
given some observed data. This is achieved by maximizing a likelihood function so that, under the assumed statistical model, the observed data is most
Maximum_likelihood_estimation
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
Nonparametric measure of rank correlation
relationship between two variables can be described using a monotonic function. The Spearman correlation between two variables is equal to the Pearson
Spearman's rank correlation coefficient
Spearman's_rank_correlation_coefficient
Process of achieving optothermal stability in optomechanical systems
glass is a function of wavelength and temperature. There are multiple formulas that can be used to define the wavelength dependence, or dispersion, of a glass
Athermalization
Graphical representation of the distribution of numerical data
and often for density estimation: estimating the probability density function of the underlying variable. The total area of a histogram used for probability
Histogram
French anthropologist and ethnologist (1934–1977)
Hobbes's discourse by reversing it; it proclaims that the machine of dispersion functions against the machine of unification; it tells us that war is against
Pierre_Clastres
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
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
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
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
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
Statistical method
choice for an approximating distribution is the empirical distribution function of the observed data. In the case where a set of observations can be assumed
Bootstrapping_(statistics)
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
Frequency with which an engineered system or component fails
function), h ( t ) {\displaystyle h(t)} . In the many-system case, this is defined as the proportional failure rate of the systems still functioning at
Failure_rate
Generates a forecast of future values of a time series
exponential window function. Whereas in the simple moving average the past observations are weighted equally, exponential functions are used to assign
Exponential_smoothing
Statistical hypothesis test
Generalized/power Geometric Harmonic Heronian Heinz Lehmer Median Mode Dispersion Average absolute deviation Coefficient of variation Interquartile range
Chi-squared_test
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
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
DISPERSION FUNCTION
DISPERSION FUNCTION
Male
Celtic
, great justiciary, or functionary.
Male
Egyptian
, a great functionary.
Girl/Female
Biblical
A stranger at Babylon, dispersion of confusion.
Girl/Female
Biblical
Removing a dissension.
Surname or Lastname
English
English : occupational name for a dresser of cloth, Old English fullere (from Latin fullo, with the addition of the English agent suffix). The Middle English successor of this word had also been reinforced by Old French fouleor, foleur, of similar origin. The work of the fuller was to scour and thicken the raw cloth by beating and trampling it in water. This surname is found mostly in southeast England and East Anglia. See also Tucker and Walker.In a few cases the name may be of German origin with the same form and meaning as 1 (from Latin fullare).Americanized version of French Fournier.Samuel Fuller (1589–1633), born in Redenhall, Norfolk, England, was among the Pilgrim Fathers who sailed on the Mayflower in 1620. He was a deacon of the church and until his death functioned as Plymouth Colony’s physician.
Male
Egyptian
, the son of the functionary Heknofre.
Biblical
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Surname or Lastname
English
English : topographic name for someone who lived by the gates of a medieval walled town. The Middle English singular gate is from the Old English plural, gatu, of geat ‘gate’ (see Yates). Since medieval gates were normally arranged in pairs, fastened in the center, the Old English plural came to function as a singular, and a new Middle English plural ending in -s was formed. In some cases the name may refer specifically to the Sussex place Eastergate (i.e. ‘eastern gate’), known also as Gates in the 13th and 14th centuries, when surnames were being acquired.Americanized spelling of German Götz (see Goetz).Translated form of French Barrière (see Barriere).In New England, Gates was the preferred English version of the name of an extensive French family, called Barrière dit Langevin.
Male
Egyptian
, an Egyptian functionary.
Girl/Female
Bengali, Hindu, Indian, Sindhi
Rainbow of Colours; Dispersion of Seven Colors
Surname or Lastname
English
English : nickname from the animal, Middle English catte ‘cat’. The word is found in similar forms in most European languages from very early times (e.g. Gaelic cath, Slavic kotu). Domestic cats were unknown in Europe in classical times, when weasels fulfilled many of their functions, for example in hunting rodents. They seem to have come from Egypt, where they were regarded as sacred animals.English : from a medieval female personal name, a short form of Catherine.Variant spelling of German and Dutch Katt.
Girl/Female
Biblical
A stranger at Babylon, dispersion of confusion.
Boy/Male
Buddhist, Indian, Japanese
Mysterious Function
Male
Egyptian
, Functionary of the Interior.
Male
Egyptian
, a high Egyptian functionary.
Biblical
removing a dissension
Biblical
a stranger at Babylon; dispersion of confusion
Surname or Lastname
English (chiefly Kent and Sussex)
English (chiefly Kent and Sussex) : occupational name for a designer or engineer, from a Middle English reduced form of Old French engineor ‘contriver’ (a derivative of engaigne ‘cunning’, ‘ingenuity’, ‘stratagem’, ‘device’). Engineers in the Middle Ages were primarily designers and builders of military machines, although in peacetime they might turn their hands to architecture and other more pacific functions.German : from the Latin personal name Januarius (see January 1). Jänner is a South German word for ‘January’, and so it is possible that this is one of the surnames acquired from words denoting months of the year, for example by converts who had been baptized in that month, people who were born or baptized in that month, or people whose taxes were due in January.
Male
Egyptian
, an Egyptian functionary.
Boy/Male
Hindu, Indian
Dispersing Darkness; Fire; Lamp; The Moon
DISPERSION FUNCTION
DISPERSION FUNCTION
Girl/Female
Tamil
Pujasatya | பà¯à®œà®¸à®¤à¯à®¯à®¾Â
Female
Danish
, war battle-maid.
Girl/Female
Hindu
Daughter, Born of the body
Surname or Lastname
English
English : perhaps a variant of Henshaw.Possibly also an Americanized spelling of German Handschuh.
Girl/Female
Spanish
Girl/Female
Hindu, Indian
Glow; Light; Splendour
Male
Scottish
Scottish Gaelic form of Norman French Robert, RAIBEART means "bright fame."
Girl/Female
Hindu
Bristi, Barsha
Boy/Male
German
Brave friend.
Surname or Lastname
English
English : habitational name from Mayland in Essex, possibly named in Old English as ‘land or estate (land) where mayweed (mægðe) grows’, or alternatively as ‘(place at) the island’, from Old English ēg-land, with the initial M- derived from a preceding ðǣm, dative case of the definite article.
DISPERSION FUNCTION
DISPERSION FUNCTION
DISPERSION FUNCTION
DISPERSION FUNCTION
DISPERSION FUNCTION
n.
The act of dissipating or dispersing; a state of dispersion or separation; dispersion; waste.
n.
Tumult; discord; dissension.
v. t. & i.
To spread or extend by dispersion.
n.
Discord; dissension.
n.
The act of turning aside from any course, occupation, or object; as, the diversion of a stream from its channel; diversion of the mind from business.
n.
The act or process of scattering or dispersing, or the state of being scattered or separated; as, the Jews in their dispersion retained their rites and ceremonies; a great dispersion of the human family took place at the building of Babel.
v. i.
Play; sport; pastime; diversion; playfulness.
n.
Dissension.
n.
A disinheriting; disherison.
n.
Natural dispersion of seeds.
n.
A Spanish diversion on horseback.
n.
The separation of light into its different colored rays, arising from their different refrangibilities.
n.
Destruction; dispersion.
v. t.
Same as Disherison.
n.
Act of disporting; diversion; play.
n.
Disagreement in opinion; dissension; controversy; quarrel; hence, cause of dissension; matter in controversy.
n.
Dissension; division; schism.
n.
Time for play or diversion.
n.
The act or result of dispersing or scattering; dispersion.
n.
Diversion; amusement; recreation.