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Statistical measure
statistics, a scale parameter is a special kind of numerical parameter of a parametric family of probability distributions. The larger the scale parameter, the
Scale_parameter
Kind of numerical parameter of a parametric family of probability distributions
that is neither a location parameter nor a scale parameter (nor a function of these, such as a rate parameter). Such a parameter must affect the shape of
Shape_parameter
Probability distribution
With a shape parameter α {\displaystyle \alpha } and a scale parameter θ With a shape parameter α {\displaystyle \alpha } and a rate parameter β = 1 /
Gamma_distribution
Method to measure temperature quantitatively
thermometer, that defines a scaling function for mapping the temperature to the measurable thermometric parameter. Such temperature scales that are purely based
Scale_of_temperature
Framework for multi-scale signal representation
image structures at different scales, by representing an image as a one-parameter family of smoothed images, the scale-space representation, parametrized
Scale_space
Bound on probability of a random variable being far from its mean
In probability theory, Chebyshev's inequality (also called the Bienaymé–Chebyshev inequality) provides an upper bound on the probability of deviation of
Chebyshev's_inequality
Quantity that indexes a parametrized family of probability distributions
roles, including the following: location parameter dispersion parameter or scale parameter shape parameter Where a probability distribution has a domain
Statistical_parameter
Statistical parameter needed for a model but not of primary interest
interest. The classic example of a nuisance parameter comes from the normal distribution, a member of the location–scale family. In the case of normal distribution
Nuisance_parameter
Topics referred to by the same term
multiplies, some quantity Long and short scales, how powers of ten are named and grouped in large numbers Scale parameter, a description of the spread or dispersion
Scale
Expansion of the universe parameter
dimensionless scale factor a {\displaystyle a} . Also known as the cosmic scale factor or sometimes the Robertson–Walker scale factor, this is a key parameter of
Scale_factor_(cosmology)
Family of probability distributions
a location–scale family is a family of probability distributions parametrized by a location parameter and a non-negative scale parameter. For any random
Location–scale_family
Concept in statistics
In statistics, a location parameter of a probability distribution is a scalar- or vector-valued parameter x 0 {\displaystyle x_{0}} , which determines
Location_parameter
Continuous probability distribution
&x\geq 0,\\0,&x<0,\end{cases}}} where k > 0 is the shape parameter and λ > 0 is the scale parameter of the distribution. Its complementary cumulative distribution
Weibull_distribution
Network whose degree distribution follows a power law
\gamma } is a parameter whose value is typically in the range 2 < γ < 3 {\textstyle 2<\gamma <3} (wherein the second moment (scale parameter) of k − γ {\displaystyle
Scale-free_network
Statistical indicators of the deviation of a sample
These robust statistics are particularly used as estimators of a scale parameter, and have the advantages of both robustness and superior efficiency
Robust_measures_of_scale
Concept in statistics
distribution, with (some of) the parameters of that distribution themselves being random variables. If the parameter is a scale parameter, the resulting mixture
Compound probability distribution
Compound_probability_distribution
Distribution of variables which satisfies a stability property under linear combinations
with this distribution has the same distribution, up to location and scale parameters. A random variable is said to be stable if its distribution is stable
Stable_distribution
Probability distribution
exponential distribution is sometimes parametrized in terms of the scale parameter β = 1/λ, which is also the mean: f ( x ; β ) = { 1 β e − x / β x ≥
Exponential_distribution
Two-parameter family of continuous probability distributions
)}}(1/x)^{\alpha +1}\exp \left(-\beta /x\right)} with shape parameter α {\displaystyle \alpha } and scale parameter β {\displaystyle \beta } . Here Γ ( ⋅ ) {\displaystyle
Inverse-gamma_distribution
Statistical law in machine learning
include the number of parameters, training dataset size, and training cost. Some models also exhibit performance gains by scaling inference through increased
Neural_scaling_law
Probability distribution
shape parameters (and a scale parameter). It is a generalization of the gamma distribution which has one shape parameter (and a scale parameter). Since
Generalized gamma distribution
Generalized_gamma_distribution
Technique for setting initial values of trainable parameters in a neural network
parameters. The choice of weight initialization method affects the speed of convergence, the scale of neural activation within the network, the scale
Weight_initialization
Probability distribution
^{2})},\quad x\geq 0,} where σ {\displaystyle \sigma } is the scale parameter of the distribution. The cumulative distribution function is F ( x
Rayleigh_distribution
Distinction between nominal, ordinal, interval and ratio variables
Level of measurement or scale of measure is a classification that describes the nature of information within the values assigned to variables. Psychologist
Level_of_measurement
Speed of convergence of a mathematical sequence
an asymptotic order q {\displaystyle q} power of a discretization scale parameter below. In general, comparatively, one sequence ( a k ) {\displaystyle
Rate_of_convergence
Integral transform
translation and scale parameter of the wavelets vary continuously. The continuous wavelet transform of a function x ( t ) {\displaystyle x(t)} at a scale a ∈ R
Continuous_wavelet_transform
Non-informative prior distribution
the Jeffreys prior. This makes it of special interest for use with scale parameters. As a concrete example, a Bernoulli distribution can be parameterized
Jeffreys_prior
Transformation method within a three-dimensional space
to use the five parameter transformation, composed of three translations, only one rotation about the Z-axis, and one change of scale. The Helmert transformation
Helmert_transformation
Probability distribution and special case of gamma distribution
(where α {\displaystyle \alpha } is the shape parameter and θ {\displaystyle \theta } the scale parameter of the gamma distribution) and X ∼ W 1 ( 1 ,
Chi-squared_distribution
Family of probability distributions often used to model tails or extreme values
of another distribution. It is specified by three parameters: location μ {\displaystyle \mu } , scale σ {\displaystyle \sigma } , and shape ξ {\displaystyle
Generalized Pareto distribution
Generalized_Pareto_distribution
Numerical parameter in probability theory
concentration parameter is a special kind of numerical parameter of a parametric family of probability distributions. Concentration parameters occur in two
Concentration_parameter
Values which describe behavior of a linear electric circuit
The S-parameters are members of a family of similar parameters, other examples being: Y-parameters and Z-parameters, H-parameters, T-parameters and ABCD-parameters
Scattering_parameters
Heavy-tail probability distribution
}}\right)^{-(\alpha +1)},\qquad x\geq 0,} with shape parameter α > 0 {\displaystyle \alpha >0} and scale parameter λ > 0 {\displaystyle \lambda >0} . The density
Lomax_distribution
Concept in statistics
estimator of the mean. When estimating a scale parameter, using a trimmed estimator as a robust measures of scale, such as to estimate the population variance
Trimmed_estimator
Gaussian distribution, that are defined by a single shape parameter and location and scale parameters, and it is not appropriate or even possible for distributions
Probability plot correlation coefficient plot
Probability_plot_correlation_coefficient_plot
Methodology for assigning prior probabilities
finite, continuous location parameter. As in the above argument, a statement that σ {\displaystyle \sigma } is a scale parameter means that the sampling distribution
Principle of transformation groups
Principle_of_transformation_groups
Name for several different families of probability distributions
{\displaystyle k>0} is the scale parameter and δ ∈ R {\displaystyle \delta \in \mathbb {R} } is the location parameter. The four-parameter family obtained thus
Generalized logistic distribution
Generalized_logistic_distribution
Statistical principle about ratio of effects to causes
\end{cases}}} where x m {\displaystyle x_{m}} is the scale parameter and α {\displaystyle \alpha } is the shape parameter. The x variable will represent wealth in
Pareto_principle
Specific probability distribution function, important in physics
(the components of the velocity vector in Euclidean space), with a scale parameter measuring speeds in units proportional to the square root of T / m
Maxwell–Boltzmann distribution
Maxwell–Boltzmann_distribution
Measure of statistical dispersion
use of the term probable error in this sense is as the name for the scale parameter of the Cauchy distribution, which does not have a standard deviation
Probable_error
Seismic intensity scale used to quantify the degree of shaking during earthquakes
more closely to seismic risk than instrumental strong-motion parameters. The MMI scale is not defined in terms of more rigorous, objectively quantifiable
Modified Mercalli intensity scale
Modified_Mercalli_intensity_scale
Topological data analysis tool
taking the sequence of Vietoris–Rips complexes over an increasing scale parameter. Often, the Vietoris–Rips filtration is used to create a discrete,
Vietoris–Rips_filtration
Middle quantile of a data set or probability distribution
median of a Cauchy distribution with location parameter x0 and scale parameter y is x0, the location parameter. The median of a power law distribution x−a
Median
Function for integral Fourier-like transform
exact time and frequency response scale to that event. The product of the uncertainties of time and frequency response scale has a lower bound. Thus, in the
Wavelet
Probability distribution
\tau ^{2},\ \nu )\ } by introducing a location parameter μ {\displaystyle \ \mu \ } and a scale parameter τ . {\displaystyle \ \tau ~.} With T ∼
Student's_t-distribution
Paradigm for the design, analysis, and scoring of tests
a} parameter stretches the horizontal scale, the b {\displaystyle b} parameter shifts the horizontal scale, and the c {\displaystyle c} parameter compresses
Item_response_theory
Continuous probability distribution
where α > 0 is a shape parameter. It can be generalised to include a location parameter m (the minimum) and a scale parameter s > 0 with the cumulative
Fréchet_distribution
Probability distribution
{\mbox{inv-}}\chi ^{2}(\nu )} , where ψ {\displaystyle \psi } is the scale parameter, equals the univariate inverse Wishart distribution W − 1 ( ψ , ν )
Scaled inverse chi-squared distribution
Scaled_inverse_chi-squared_distribution
Continuous probability distribution for a non-negative random variable
interpretable parameters and a simple form for the cumulative distribution function [1]. The parameter α > 0 {\displaystyle \alpha >0} is a scale parameter and
Log-logistic_distribution
Probability distribution
gamma distribution is the generalization of the beta prime when the scale parameter, q is added, but where p = 1. It is so named because it is formed by
Beta_prime_distribution
Measure of a civilization's evolution
The Kardashev scale (Russian: шкала Кардашёва, romanized: shkala Kardashova) is a method of measuring a civilization's level of technological advancement
Kardashev_scale
Statistical model for a binary dependent variable
variables multiplicatively scales the odds of the given outcome at a constant rate, with each independent variable having its own parameter; for a binary dependent
Logistic_regression
Parameter introduced by the Minor Planet Center
uncertainty of a perturbed orbital solution for a minor planet. The parameter is a logarithmic scale from 0 to 9 that measures the anticipated longitudinal uncertainty
Uncertainty_parameter
Statistical distribution
Nakagami distributions has two parameters: a shape parameter m ≥ 1 / 2 {\displaystyle m\geq 1/2} and a scale parameter Ω > 0 {\displaystyle \Omega >0}
Nakagami_distribution
Topic in probability theory and statistics
distribution with location parameter x = 0 and scale parameter γ = 1. A Burr distribution with parameters c = 1 and k (and scale λ) is a Lomax distribution
Relationships among probability distributions
Relationships_among_probability_distributions
Probability distribution
is the location parameter, specifying the location of the peak of the distribution, and γ {\displaystyle \gamma } is the scale parameter which specifies
Cauchy_distribution
Large language model developed by Google
trained smaller versions of PaLM (with 8 and 62 billion parameters) to test the effects of model scale. PaLM is capable of a wide range of tasks, including
PaLM
Concept in Bayesian statistics
that is a uniform flat distribution; and also if the unknown parameter is a scale parameter (i.e. the forward probability function has the form P r ( x
Credible_interval
Kurtosis of the order parameter in statistical physics
The Binder parameter or Binder cumulant in statistical physics, also known as the fourth-order cumulant U L = 1 − ⟨ s 4 ⟩ L 3 ⟨ s 2 ⟩ L 2 {\displaystyle
Binder_parameter
Different meanings for numbers
Much of the world has adopted either the short or long scale. Countries using the long scale include most countries in continental Europe and most that
Long_and_short_scales
Generative linguistics framework
Principles and parameters is a framework within generative linguistics in which the syntax of a natural language is described in accordance with general
Principles_and_parameters
Measure of the strength of earthquakes
The Richter scale (/ˈrɪktər/), also called the Richter magnitude scale, Richter's magnitude scale, and the Gutenberg–Richter scale, is a measure of the
Richter_scale
Scale for rating tornado intensity
The EF scale also improved damage parameter descriptions.[citation needed] The original scale as derived by Fujita was a theoretical 13-level scale (F0–F12)
Fujita_scale
Geodetic reference system
determine local-to-geocentric datum shifts, datum rotation parameters, a datum scale parameter, and a value for the semimajor axis of the WGS Ellipsoid
World_Geodetic_System
Discrete probability distribution
is the quantile function of a gamma distribution with shape parameter n and scale parameter 1. This interval is 'exact' in the sense that its coverage
Poisson_distribution
Scale for rating tornado intensity
The TORRO tornado intensity scale (or T-Scale) is a scale measuring tornado intensity between T0 and T11. It was proposed by Terence Meaden of the Tornado
TORRO_scale
Conventional name of the gamma distribution when applied to macromolecular polydispersity
and in 1948 by Bruno H. Zimm. This distribution has only a shape parameter k, the scale being fixed at θ=1/k. Accordingly, the probability density function
Schulz–Zimm_distribution
Allergy rating system
(15 November 2025). "Unveiling hidden allergenic hotspots: A fine-scale, parameter optimized approach for spatiotemporal mapping of urban allergenicity
Ogren_Plant_Allergy_Scale
Probability distribution
X, and α is a positive parameter. The type I Pareto distribution is characterized by a scale parameter xm and a shape parameter α, which is known as the
Pareto_distribution
{x^{2}}{2t}}}} and the standard deviation of the Gaussian σ is related to the scale parameter t according to t = σ2. Separability will be assumed in all that follows
Scale_space_implementation
SI unit of temperature
K}})}{\log({\text{373 K}}/{\text{273 K}})}}} The parameters of the scale were arbitrarily chosen to coincide with the Celsius scale at 0° and 100 °C or 273 and 373 K
Kelvin
Type of probability distribution
} the scale parameter σ 2 {\displaystyle \sigma ^{2}} of the truncated normal distribution is allowed to assume negative values. The parameter σ {\displaystyle
Truncated_normal_distribution
x < 0. Here k > 0 is the first shape parameter, α > 0 is the second shape parameter and λ > 0 is the scale parameter of the distribution. The density is
Exponentiated Weibull distribution
Exponentiated_Weibull_distribution
Machine learning calibration technique
classifier output f(x), where A and B are two scalar parameters that are learned by the algorithm. After scaling, values can be predicted as y = 1 iff P ( y
Platt_scaling
Parameter-efficient fine-tuning technique for large language models
million parameters, cost less than $50,000 to train. GPT-2, released in 2019 with 1.5 billion parameters, required $40,000 to train. By 2020, GPT-3 scaled to
LoRA_(machine_learning)
estimator of the mean. When estimating a scale parameter, such as when using an L-estimator as a robust measures of scale, such as to estimate the population
L-estimator
this combination, the number of parameters to be analyzed is reduced and the results may be obtained in terms of the scaled variables. In addition to reducing
Non-dimensionalization and scaling of the Navier–Stokes equations
Non-dimensionalization_and_scaling_of_the_Navier–Stokes_equations
Tensor related to gradients
one-parameter scale-space features an image descriptor that is defined over two scale parameters. One scale parameter, referred to as local scale t {\displaystyle
Structure_tensor
Fourth standardized moment in statistics
{x}{a}}\right)^{2}\right]^{-m},} where a is a scale parameter and m is a shape parameter. All densities in this family are symmetric. The k-th
Kurtosis
Normally distributed deviate
pseudorandom number sequence) by multiplying by the scale parameter and adding the location parameter. More generally, the generation of pseudorandom number
Standard_normal_deviate
Continuous probability distribution
{x-\mu }{2s}}\right).} In this equation μ is the mean, and s is a scale parameter proportional to the standard deviation. The probability density function
Logistic_distribution
Family of continuous probability distributions
equivalent, parametrization uses the scale parameter β {\displaystyle \beta } , which is the reciprocal of the rate parameter (i.e., β = 1 / λ {\displaystyle
Erlang_distribution
Family of continuous probability distributions
real p {\displaystyle p} ) can serve as a scale parameter, so a proper (i.e., unscaled) shape parameter would be any non-zero power of φ = λ / μ {\displaystyle
Inverse_Gaussian_distribution
layer thickness parameters, generally denoted as δ ( x ) {\displaystyle \delta (x)} , are used to describe characteristic thickness scales in the boundary
Boundary_layer_thickness
Cosmological time duration
these parameters, the age of the universe can be determined by using the Friedmann equation. This equation relates the rate of change in the scale factor
Age_of_the_universe
Type of statistical model
\beta } is the shape parameter, λ {\displaystyle \lambda } is the scale parameter and μ {\displaystyle \mu } is the location parameter. The binomial model
Parametric_model
Probability distribution
inverse-gamma distribution. with shape parameter α = ν 2 {\displaystyle \alpha ={\frac {\nu }{2}}} and scale parameter β = 1 2 {\displaystyle \beta ={\frac
Inverse-chi-squared distribution
Inverse-chi-squared_distribution
coupling parameter of the resonator specifies the part of the energy of the laser field, which is output at each round-trip. The coupling parameter should
Coupling_parameter
Continuous probability distribution
}}x\geq m\end{cases}}} Here, m is a location parameter, λ > 0 is a scale parameter, and κ is an asymmetry parameter. When κ = 1, (x-m)s κs simplifies to |x-m|
Asymmetric Laplace distribution
Asymmetric_Laplace_distribution
Factor in X-ray crystallography
I(hkl)=(1-x)|F(hkl)|^{2}+x|F(-h-k-l)|^{2}} where x is the Flack parameter, I is the square of the scaled observed structure factor and F is the calculated structure
Flack_parameter
Approach used in computer vision systems
choice of the local scale parameter t {\displaystyle t} and the integration scale parameter s {\displaystyle s} , these scale parameters are usually coupled
Corner_detection
Dimensionless measure in cosmology
The deceleration parameter q {\displaystyle q} in cosmology is a dimensionless measure of the cosmic acceleration of the expansion of space in a
Deceleration_parameter
Family of stochastic processes
number α {\displaystyle \alpha } called the concentration parameter (also known as scaling parameter). The base distribution is the expected value of the process
Dirichlet_process
Features that do not change if length or energy scales are multiplied by a common factor
theory is scale-invariant in D = 4, the quantized version is not scale-invariant. We can see this from the beta-function for the coupling parameter, g. Even
Scale_invariance
Probability distribution
location parameter of the underlying (non-standardized) Student's t-distribution, σ ^ {\displaystyle {\hat {\sigma }}} is the scale parameter of the underlying
Log-t_distribution
Probability distribution
of two independent Cauchy distributions (with the same scale parameter and the location parameter set to zero) will give the same distribution. This becomes
Ratio_distribution
Statistics models class
_{j}S_{j}\beta /(2\phi )\}} (where ϕ {\displaystyle \phi } is the GLM scale parameter introduced only for later convenience), but we can immediately recognize
Generalized_additive_model
Measure of earthquake size
seismological parameter it is based on, is not measured routinely for smaller quakes. For example, the United States Geological Survey does not use this scale for
Moment_magnitude_scale
Theory in statistics
is a three-parameter family of continuous probability distributions. It has a location parameter μ {\displaystyle \mu } , scale parameter θ {\displaystyle
Normal-exponential-gamma distribution
Normal-exponential-gamma_distribution
Non-dimensional number in fluid dynamics
the American fluid dynamicist Hunter Rouse. It is a characteristic scale parameter in the Rouse Profile of suspended sediment concentration with depth
Rouse_number
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SCALE PARAMETER
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SCALE PARAMETER
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