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Kind of numerical parameter of a parametric family of probability distributions
probability theory and statistics, a shape parameter (also known as form parameter) is a kind of numerical parameter of a parametric family of probability
Shape_parameter
Statistical measure
a scale parameter is a special kind of numerical parameter of a parametric family of probability distributions. The larger the scale parameter, the more
Scale_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
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
Probability distribution
parameters, denoted by alpha (α) and beta (β), that appear as exponents of the variable and its complement to 1, respectively, and control the shape of
Beta_distribution
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
Variable used for specification
that describe the system are called parameters. For example, in mechanics, the masses, the dimensions and shapes (for solid bodies), the densities and
Parameter
Method in approximation theory
{\displaystyle \varphi (r)=\exp(-(\varepsilon r)^{2})} , the Gaussian, with a shape parameter of ε = 3 {\displaystyle \varepsilon =3} , we can then solve the matrix
Radial basis function interpolation
Radial_basis_function_interpolation
Family of probability distributions often used to model tails or extreme values
is specified by only scale and shape and sometimes only by its shape parameter. Some references give the shape parameter as κ = − ξ {\displaystyle \kappa
Generalized Pareto distribution
Generalized_Pareto_distribution
Probability distribution
continuous probability distributions on the real line. Both families add a shape parameter to the normal distribution. To distinguish the two families, they are
Generalized normal distribution
Generalized_normal_distribution
Local and global geometry of the universe
to find the shape of space': scientists wonder if the universe is like a doughnut". The Guardian. Retrieved 25 May 2026. "Density Parameter, Omega". hyperphysics
Shape_of_the_universe
Probability distribution
depending on the author, either the parameter r or its reciprocal α is referred to as the "dispersion parameter", "shape parameter" or "clustering coefficient"
Negative binomial distribution
Negative_binomial_distribution
Family of continuous probability distributions
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
Concept in statistics
distribution has exponential tails and a Pareto distribution has long tails. Shape parameter List of probability distributions Yule, G.U., Kendall, M.G. (1950)
Shape of a probability distribution
Shape_of_a_probability_distribution
Probability distribution
\Gamma \left(N,{\frac {1}{2\sigma ^{2}}}\right)} with integer shape parameter N and rate parameter 1 2 σ 2 . {\displaystyle {\frac {1}{2\sigma ^{2}}}.} [ Y
Rayleigh_distribution
Feature observed in spectroscopy
line shapes include Lorentzian, Gaussian and Voigt functions, whose parameters are the line position, maximum height and half-width. Actual line shapes are
Spectral_line_shape
Conventional name of the gamma distribution when applied to macromolecular polydispersity
Schulz 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
Schulz–Zimm_distribution
Set of values that describe the polarization state of electromagnetic radiation
total intensity (I), (fractional) degree of polarization (p), and the shape parameters of the polarization ellipse. The effect of an optical system on the
Stokes_parameters
Symmetric probability distribution
single shape parameter, λ, and as with other probability distributions, it can be transformed with a location parameter, μ, and a scale parameter, σ. Since
Tukey_lambda_distribution
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
Stochastic process for effort or wear
represents the time from 0. The shape parameter γ {\displaystyle \gamma } (inversely) controls the jump size, and the rate parameter λ {\displaystyle \lambda
Gamma_process
Mathematical function having a characteristic S-shaped curve or sigmoid curve
1 {\displaystyle \alpha <1} and β < 1 {\displaystyle \beta <1} are shape parameters. Smooth transition function normalized to (−1,1): f ( x ) = { 2 1 +
Sigmoid_function
Probability distribution
two 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
Continuous probability distribution for a non-negative random variable
is also the median of the distribution. The parameter β > 0 {\displaystyle \beta >0} is a shape parameter. The distribution is unimodal when β > 1 {\displaystyle
Log-logistic_distribution
Family of probability distributions related to the normal distribution
Weibull distribution with fixed shape parameter k is an exponential family. Unlike in the previous examples, the shape parameter does not affect the support;
Exponential_family
Technique for the characterisation of crystalline materials
of many free parameters, including peak shape, unit cell dimensions and coordinates of all atoms in the crystal structure. Other parameters can be guessed
Rietveld_refinement
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
Generalization of gamma distribution to multiple dimensions
shown that the Wishart distribution can be defined if and only if the shape parameter n belongs to the set Λ p := { 0 , … , p − 1 } ∪ ( p − 1 , ∞ ) . {\displaystyle
Wishart_distribution
Continuous probability distribution
}}~x>0~.} 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
continuously and independently at a constant average rate; the distance parameter could be any meaningful mono-dimensional measure of the process, such
Exponential_distribution
Topics referred to by the same term
including: The compactness measure of a shape In statistics: The shape parameter, sometimes referred to as the shape factor, of some probability distributions
Shape_factor
Name for several different families of probability distributions
distribution, with support x ∈ R {\displaystyle x\in \mathbb {R} } and shape parameters α , β > 0 {\displaystyle \alpha ,\beta >0} , has (as shown above) the
Generalized logistic distribution
Generalized_logistic_distribution
Parameters that define a specific orbit
Other parameters can also be used to describe the size and shape of an orbit, such as the linear eccentricity, flattening, and focal parameter, but the
Orbital_elements
distribution, which is a special case of the gamma distribution with integral shape parameter, developed to predict waiting times in queuing systems The inverse-gamma
List of probability distributions
List_of_probability_distributions
Comparison of two distributions
graphical means of estimating parameters in a location-scale family of distributions. A Q–Q plot is used to compare the shapes of distributions, providing
Q–Q_plot
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
This page describes some of the parameters used to characterize the thickness and shape of boundary layers formed by fluid flowing along a solid surface
Boundary_layer_thickness
Topics referred to by the same term
instrument onboard propulsion module of Chandrayaan-3 shape parameter a kind of numerical parameter for a parametric family of probability distributions
Shape_(disambiguation)
as an extension of the Weibull family obtained by adding a second shape parameter. The cumulative distribution function for the exponentiated Weibull
Exponentiated Weibull distribution
Exponentiated_Weibull_distribution
Type of mathematical function
distribution if both shape parameters are ≥ 1, and the Weibull distribution if the shape parameter is ≥ 1. Note that all of the parameter restrictions have
Logarithmically concave function
Logarithmically_concave_function
Probability distribution and special case of gamma distribution
=2)} (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
Kurtosis of the order parameter in statistical physics
at the critical point, the value of the Binder parameter depends on boundary conditions, the shape of the system, and anisotropy of correlations. A
Binder_parameter
Family of continuous probability distributions
\lambda \geq 0,} The parameter k is called the shape parameter, and the parameter λ {\displaystyle \lambda } is called the rate parameter. An alternative,
Erlang_distribution
Topic in probability theory and statistics
with shape parameter k = 1 and rate parameter β is an exponential distribution with rate parameter β. A beta distribution with shape parameters α = β
Relationships among probability distributions
Relationships_among_probability_distributions
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
Statistical principle about ratio of effects to causes
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 (e
Pareto_principle
Three-parameter family of continuous probability distributions
gamma distributions is used, such that the parameters are: the mean of the distribution, the usual shape parameter. K-distribution is a special case of variance-gamma
K-distribution
Probability distribution
X | ) = γ {\displaystyle \operatorname {median} (|X|)=\gamma } the shape parameter. Cauchy ( 0 , 1 ) ∼ t ( d f = 1 ) {\displaystyle \operatorname {Cauchy}
Cauchy_distribution
Probability distribution
known as a Pareto Type II distribution, with shape parameter α {\displaystyle \alpha } and scale parameter λ {\displaystyle \lambda } , then X λ ∼ β ′
Beta_prime_distribution
Type of mathematical function
_{i}\right\|} and using ε {\textstyle \varepsilon } to indicate a shape parameter that can be used to scale the input of the radial kernel): Infinitely
Radial_basis_function
Discrete probability distribution
1)} 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
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 moment
Kurtosis
force caused by the spherical shape of the Earth. It is important in the generation of Rossby waves. The Rossby parameter β {\displaystyle \beta } is given
Rossby_parameter
Middle quantile of a data set or probability distribution
rate parameter λ is the natural logarithm of 2 divided by the rate parameter: λ−1ln 2. The median of a Weibull distribution with shape parameter k and
Median
1997 studio album by Foo Fighters
The Colour and the Shape is the second studio album by American rock band Foo Fighters, released on May 20, 1997, by Roswell and Capitol Records. It was
The_Colour_and_the_Shape
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
Area of mathematics
changes of the behaviour of the system. However, examined in a larger parameter space, catastrophe theory reveals that such bifurcation points tend to
Catastrophe_theory
Family of closed mathematical curves
and n is a positive parameter that defines the shape. When n = 2, the superellipse is an ordinary ellipse. For n > 2, the shape is more rectangular with
Superellipse
(concentration, asymmetry, smoothness) parameters are a tool originally developed in astronomy to characterize the shapes and images of objects with some central
CAS_parameters
Probability distribution
distribution with four shape parameters, including more than thirty named distributions as limiting or special cases. A fifth parameter for scaling is sometimes
Generalized_beta_distribution
Mathematical model of the Big Bang
model is based on six parameters: baryon density parameter; dark matter density parameter; scalar spectral index; two parameters related to curvature fluctuation
Lambda-CDM_model
coefficient (PPCC) plot is a graphical technique for identifying the shape parameter for a distributional family that best describes the data set. This
Probability plot correlation coefficient plot
Probability_plot_correlation_coefficient_plot
Shape
operate with various modifications of oval shapes when a unit length (L = 1) is used, and the oval parameters are presented as their combinations conventionally
Oval
Polyhedron with eight triangular faces
Futamura, F.; Frantz, M.; Crannell, A. (2014). "The cross ratio as a shape parameter for Dürer's solid". Journal of Mathematics and the Arts. 8 (3–4): 111–119
Octahedron
Distributional regression model
(target) variable but the parameters of this distribution can vary according to explanatory variables. Therefore the shape of this distribution for the
Generalized additive model for location, scale and shape
Generalized_additive_model_for_location,_scale_and_shape
Type of scattering resonance
an asymmetric line-shape. Interference between a background and a resonant scattering process produces the asymmetric line-shape. It is named after Italian-American
Fano_resonance
Empirical law on the variance of species in a habitat
the canonical and index parameters, respectively. These last two parameters are analogous to the scale and shape parameters used in probability theory
Taylor's_law
Probability distribution
has a logistic distribution. The shift parameter adds a location parameter to the scale and shape parameters of the (unshifted) log-logistic. The properties
Shifted log-logistic distribution
Shifted_log-logistic_distribution
Software design pattern
template parameter (T in Counter<T>) and the reason why we cannot use a simple un-templated base class. Method chaining, also known as named parameter idiom
Curiously recurring template pattern
Curiously_recurring_template_pattern
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
Object categorization problem
then clustered, yielding a number of features (the clusters) and the shape parameter X {\displaystyle X} , composed of the cluster centers. The Kadir–Brady
One-shot learning (computer vision)
One-shot_learning_(computer_vision)
Concept in astrodynamics
hyperbolic orbit other parameters may be more useful in understanding a body's motion. The following table lists the main parameters describing the path
Hyperbolic_trajectory
Dimensionless measure of a porous material's permeability
shape of each relative permeability curve, the shape parameter N. The LET-correlation adds more degrees of freedom in order to accommodate the shape of
Relative_permeability
General shape of a human body
Human body shape is a complex phenomenon with sophisticated detail and function. The general shape or figure of a person is defined mainly by the molding
Body_shape
Theory in statistics
{\displaystyle \mu } , scale parameter θ {\displaystyle \theta } and a shape parameter k {\displaystyle k} . The probability density function (pdf) of the
Normal-exponential-gamma distribution
Normal-exponential-gamma_distribution
Study of relationship of energy with formation of micelles
solvent. The shape of a micelle is directly dependent on the packing parameter of the surfactant. Surfactants with a packing parameter of N S {\displaystyle
Thermodynamics of micellization
Thermodynamics_of_micellization
Continuous probability distribution, named after Benjamin Gompertz
0 {\displaystyle b>0\,\!} is the scale parameter and η > 0 {\displaystyle \eta >0\,\!} is the shape parameter of the Gompertz distribution. In the actuarial
Gompertz_distribution
Inverse of the average of the inverses of a set of numbers
H=k\left(1+{\frac {1}{\alpha }}\right)} where k is the scale parameter and α is the shape parameter. For a random sample, the harmonic mean is calculated as
Harmonic_mean
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
Equations in physical cosmology
The first Friedmann equation contains the discrete parameter k, the value of which determines the shape of the universe: +1 is a 3-sphere, the universe is
Friedmann_equations
Plane curve
the variable names x {\displaystyle x} and y {\displaystyle y} and the parameter names a {\displaystyle a} and b . {\displaystyle b.} This is the distance
Ellipse
Cosmological time duration
described by a number of other parameters, but for the purpose of computing its age these three, along with the Hubble parameter H 0 {\displaystyle ~H_{0}~}
Age_of_the_universe
observables include: The sphericity; The aplanarity; The thrust. The C-parameter; The jet broadening. V. D. Barger, R. J. N. Phillips (1997) “Collider
Event_shape_observables
Set of electromechanical parameters
Thiele/Small parameters (commonly abbreviated T/S parameters, or TSP) are a set of electromechanical parameters that define the specified low frequency
Thiele/Small_parameters
Method of representing curves and surfaces in computer graphics
interaction. NURBS surfaces are functions of two parameters mapping to a surface in three-dimensional space. The shape of the surface is determined by control
Non-uniform_rational_B-spline
Class of probability distributions
fixed scale parameter, and thus is also an exponential family but not a NEF (note that only a gamma distribution with fixed shape parameter is a NEF).
Natural_exponential_family
Probability distribution
interaction between the Dirichlet shape parameters α {\displaystyle {\boldsymbol {\alpha }}} , and the transformation parameters a , b {\displaystyle a,\mathbf
Dirichlet_distribution
Concept in chemistry
Hansen solubility parameters were developed by Charles M. Hansen in his Ph.D thesis in 1967 as a way of predicting if one material will dissolve in another
Hansen_solubility_parameter
Concept in celestial mechanics
gravitational parameter μ of a celestial body is the product of the gravitational constant G and the mass M of that body. For two bodies, the parameter may be
Standard gravitational parameter
Standard_gravitational_parameter
System for describing queueing models
of parameter λ. The second M means that the service time is Markovian: it follows an exponential distribution of parameter μ. The last parameter is the
Kendall's_notation
Alloy which returns to a preset shape when heated
metallurgy, a shape-memory alloy (SMA) is an alloy that can be deformed when cold but returns to its pre-deformed ("remembered") shape when heated. It
Shape-memory_alloy
Statistical quantity
S={\frac {2}{\beta ^{2}(4+5\alpha ^{2})}}} where α is the shape parameter and β is the location parameter. Cantor distribution: despite the distribution being
Nonparametric_skew
Probability distribution in physics
distribution with the index of stability or shape parameter α {\displaystyle \alpha } equal to 3/2 and the skewness parameter β {\displaystyle \beta } of zero.
Holtsmark_distribution
Family of geometric shapes
squareness parameter ϵ 2 {\displaystyle \epsilon _{2}} , and whose vertical sections through the center are superellipses with the squareness parameter ϵ 1 {\displaystyle
Superellipsoid
Problem in recreational mathematics
a problem of constructing a planar curve in the shape of an elephant from only four fixed parameters. It originated from a discussion between physicists
Von_Neumann's_elephant
Quadrilateral symmetric across a diagonal
The behavior of outer billiards on any kite depends strongly on the parameter α {\displaystyle \alpha } and in particular whether it is rational. For
Kite_(geometry)
Statistical indicators in signal processing
indicates the similarity of the shape of the signal to a pure sine wave. Since the calculation of the Hjorth parameters is based on variance, the computational
Hjorth_parameters
Modification using the principle of template matching
An algorithm can compute the best set of parameters for a given shape from edge pixel data. These parameters do not have equal status. The reference origin
Generalised_Hough_transform
Engineering design method
parameters, new shapes are created simultaneously. In parametric design software, designers and engineers are free to add and adjust the parameters that
Parametric_design
Family of probability distributions
{1}{|\xi |}}\ ,\end{cases}}} where ξ , {\displaystyle \ \xi \ ,} the shape parameter, can be any real number. Thus, for ξ > 0 , {\displaystyle \ \xi
Generalized extreme value distribution
Generalized_extreme_value_distribution
SHAPE PARAMETER
SHAPE PARAMETER
Male
English
Anglicized form of Irish Gaelic Seán, SHANE means "God is gracious."
Girl/Female
Indian
Shape
Girl/Female
Tamil
Shape
Boy/Male
Hindu, Indian
Shape
Boy/Male
Irish
Irish form of John meaning “â€God’s gracious gift.â€â€ Shane is a very popular variant of the name in Northern Ireland in memory of Shane O’Neill whose forces won notable victories over the armies of Queen Elizabeth 1st in the sixteenth century.
Girl/Female
Tamil
Shape
Boy/Male
Assamese, Bengali, Gujarati, Hindu, Indian, Kannada, Tamil
Shape
Girl/Female
Gujarati, Hindu, Indian, Sikh
Shape
Surname or Lastname
English
English : topographic name from Middle English slape ‘slippery, miry place’, or a habitational name from any of the places named with this word (Old English slǣp), as for example Slape in Dorset or Sleap in Shropshire.
Boy/Male
Tamil
Shape
Female
English
Feminine variant spelling of English unisex Shea, probably SHAE means "hawk-like."Â
Boy/Male
Hindu, Indian
Shape
Boy/Male
Hindi
Shape.
Male
English
Variant spelling of English unisex Shea, possibly SHAYE means "hawk-like."
Boy/Male
Tamil
Shape
Girl/Female
Hindu, Indian, Tamil, Telugu
Shape
Girl/Female
Indian, Punjabi, Sikh
Shape
Girl/Female
Hindu, Indian
Shape
Surname or Lastname
English and Scottish
English and Scottish : habitational name from any of various places in England and southern Scotland, for example in North Yorkshire near Bedale, in the Lowlands near Biggar, and in Suffolk, so named with Old English snæp ‘area of boggy land’. In Sussex the dialect term snape is still used of boggy, uncultivable land.
Girl/Female
Hindu, Indian, Tamil, Telugu
Shape
SHAPE PARAMETER
SHAPE PARAMETER
Male
Serbian
(Вукашин) Serbian name VUKASIN means "wolf."
Surname or Lastname
English
English : habitational name from any of various places now called Wingfield. North and South Wingfield in Derbyshire are evidently named with Old English wynn ‘meadow’, ‘pasture’ + feld ‘pasture’, ‘open country’. A place of this name in Bedfordshire may have as it first element a topographical term or bird name wince (see Winch). One in Suffolk was probably either the ‘field of the people of Wīga’ (a short form of any of various compound names formed with wīg ‘war’), or else derives its first element from Old English wēoh ‘(pre-Christian) temple’.
Boy/Male
Indian
One who sleeps
Boy/Male
Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Moon
Girl/Female
Hindu, Indian
Kindness
Surname or Lastname
English
English : nickname from Middle English pode ‘toad’.
Girl/Female
Arabic, Indian, Kannada, Muslim
Of Beautiful Face and Body
Boy/Male
Hebrew Biblical
God has taken.
Girl/Female
Australian, French, German, Latin
Little; Small; Female Version of Paul
Boy/Male
Hindu, Indian, Marathi
Long Lived
SHAPE PARAMETER
SHAPE PARAMETER
SHAPE PARAMETER
SHAPE PARAMETER
SHAPE PARAMETER
imp.
of Shape
n.
Character or construction of a thing as determining its external appearance; outward aspect; make; figure; form; guise; as, the shape of a tree; the shape of the head; an elegant shape.
a.
Shaped like a strap; ligulate; as, a strap-shaped corolla.
n.
One who shapes; as, the shaper of one's fortunes.
a.
Having the form or shape of a kidney; reniform; as, a kidney-shaped leaf.
a.
Having the shape of a wide-mouthed bell; campanulate.
a.
Having the shape of a spindle.
n.
To be ashamed; to feel shame.
a.
Having the shape of a horn; horn-shaped.
a.
Having the shape of an urn; as, the urn-shaped capsules of some mosses.
a.
Of a linear shape.
a.
Having the shape of a wedge; cuneiform.
n.
To adapt to a purpose; to regulate; to adjust; to direct; as, to shape the course of a vessel.
a.
Having the shape of a top; (Bot.) cone-shaped, with the apex downward; turbinate.
p. p.
of Shape