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Distribution of variables which satisfies a stability property under linear combinations
to be stable if its distribution is stable. The stable distribution family is also sometimes referred to as the Lévy alpha-stable distribution, after
Stable_distribution
Mandelbrot first used the stable (or α {\displaystyle \alpha } -stable) distribution to model the empirical distributions which have the skewness and
Financial models with long-tailed distributions and volatility clustering
Financial_models_with_long-tailed_distributions_and_volatility_clustering
Probability distribution
case of the inverse-gamma distribution and a stable distribution. The probability density function of the Lévy distribution over the domain x ≥ μ {\displaystyle
Lévy_distribution
Discrete-stable distributions are a class of probability distributions with the property that the sum of several random variables from such a distribution under
Discrete-stable_distribution
Probability distribution
limiting case, all stable distributions have heavy tails and infinite variance. It is one of the few distributions that are stable and that have probability
Normal_distribution
Concept in probability theory
multivariate stable distribution is a multivariate probability distribution that is a multivariate generalisation of the univariate stable distribution. The multivariate
Multivariate stable distribution
Multivariate_stable_distribution
Probability distribution
the few stable distributions with a probability density function that can be expressed analytically, the others being the normal distribution and the
Cauchy_distribution
Generalization of the one-dimensional normal distribution to higher dimensions
spherically symmetric multivariate distribution. Multivariate stable distribution extension of the multivariate normal distribution, when the index (exponent in
Multivariate normal distribution
Multivariate_normal_distribution
The Johnson SU distribution The Landau distribution The Laplace distribution The Lévy skew alpha-stable distribution or stable distribution is a family of
List of probability distributions
List_of_probability_distributions
Index of articles associated with the same name
stationary (marginal) distribution, although in probability and statistics the term has a rather different meaning: see stable distribution. Crudely stated
Stationary_distribution
Probability distribution
such as mean or variance, are undefined. The distribution is a particular case of stable distribution. The probability density function, as written originally
Landau_distribution
Probability distribution
X ∼ GeometricStable ( 2 , 0 , λ , 0 ) {\displaystyle X\sim {\textrm {GeometricStable}}(2,0,\lambda ,0)} (geometric stable distribution) then X ∼ Laplace
Laplace_distribution
Random walk with heavy-tailed step lengths
is a random walk in which the step-lengths have a stable distribution, a probability distribution that is heavy-tailed. When defined as a walk in a space
Lévy_flight
Family of probability distributions
2, gamma distribution, p = 2, positive stable distributions, 2 < p < 3, Inverse Gaussian distribution, p = 3, positive stable distributions, p > 3, and
Tweedie_distribution
Discrete probability distribution
Poisson distribution is named after French mathematician Siméon Denis Poisson. It plays an important role for discrete-stable distributions. Under a
Poisson_distribution
Probability distribution
t-distribution; The family of stable distributions, excepting the special case of the normal distribution within that family. Some stable distributions
Heavy-tailed_distribution
Probability distribution
geometric stable distribution or geo-stable distribution is a type of leptokurtic probability distribution. These distributions are analogues for stable distributions
Geometric_stable_distribution
French mathematician (1886-1971)
local time, stable distributions and characteristic functions. Lévy processes, Lévy flights, Lévy measures, Lévy's constant, the Lévy distribution, the Lévy
Paul_Lévy_(mathematician)
Fundamental theorem in probability theory and statistics
b_{n}.} Distributions Ξ which can arise in this way are called stable. Clearly, the normal distribution is stable, but there are also other stable distributions
Central_limit_theorem
Family of probability distributions
value distribution is a special case of a max-stable distribution, and is a transformation of a min-stable distribution. The GEV distribution is widely
Generalized extreme value distribution
Generalized_extreme_value_distribution
Community-supported Linux distribution
Tumbleweed, an upstream rolling release distribution, and Leap, a stable release distribution which is sourced from SUSE Linux Enterprise. The openSUSE project
OpenSUSE
stable process is a type of stochastic process. It includes stochastic processes whose associated probability distributions are stable distributions.
Stable_process
Continuous probability distribution
Frechet distribution is a max stable distribution The negative of a random variable having a Frechet distribution is a min stable distribution The cumulative
Fréchet_distribution
Probability distribution with high skewness or kurtosis
shortcoming of the normal distribution model and have proposed that fat-tailed distributions such as the stable distributions govern asset returns frequently
Fat-tailed_distribution
Free general-purpose operating system
releases, distributions or suites) are regularly maintained: Stable is the current release and targets stable and well-tested software needs. Stable is made
Debian
Algorithmic technique using hashing
a d-dimensional vector with entries chosen independently from a stable distribution and b {\displaystyle b} is a real number chosen uniformly from the
Locality-sensitive_hashing
When the linear combination of a random variable with itself has the same distribution
same distribution, up to location and scale parameters. The distributions of random variables having this property are said to be "stable distributions".
Stability_(probability)
Technique for the generative modeling of a continuous probability distribution
after a long time, the cloud of particles would settle into the stable distribution of N ( 0 , I ) {\displaystyle {\mathcal {N}}(0,I)} . Let ρ t {\displaystyle
Diffusion_model
Particular case of the generalized extreme value distribution
statistics, the Gumbel distribution (also known as the type-I generalized extreme value distribution) is used to model the distribution of the maximum (or
Gumbel_distribution
Probability distribution in physics
(one-dimensional) Holtsmark distribution is a continuous probability distribution. The Holtsmark distribution is a special case of a stable distribution with the index
Holtsmark_distribution
Probability distribution
statistics, the Lindley distribution is a continuous probability distribution for nonnegative-valued random variables. The distribution is named after Dennis
Lindley_distribution
Lightweight systemd free Linux distribution
antiX (/ˈæntɪks/) is a Linux distribution, originally based on MEPIS, which itself is based on the Debian Stable distribution. antiX initially replaced the
AntiX
Functional relationship between two quantities
Low-degree saturation Pareto distribution Power-law fluid Simon model Stable distribution Stevens's power law Notes Yaneer Bar-Yam. "Concepts: Power Law".
Power_law
Spectral density of light emitted by a black body
expressed as an energy distribution, it is the unique stable distribution for radiation in thermodynamic equilibrium. As an energy distribution, it is one of a
Planck's_law
Type of probability distribution
Named joint distributions that arise frequently in statistics include the multivariate normal distribution, the multivariate stable distribution, the multinomial
Joint probability distribution
Joint_probability_distribution
Probability distribution
Laplace distribution, including the special case of μ = 0 {\displaystyle {\boldsymbol {\mu }}=\mathbf {0} } , is an example of a geometric stable distribution
Multivariate Laplace distribution
Multivariate_Laplace_distribution
French-American mathematician (1924–2010)
Gaussian distribution, but rather Lévy stable distributions having infinite variance. He found, for example, that cotton prices followed a Lévy stable distribution
Benoit_Mandelbrot
Two kinds of probability distributions
, the expectation is infinite. In addition, these distributions are geometric stable distributions. Parameter estimation procedures can be found here
Mittag-Leffler_distribution
Limiting set in dynamical systems
Cycle detection Hyperbolic set Stable manifold Steady state Wada basin Hidden oscillation Rössler attractor Stable distribution Convergent evolution Desprez
Attractor
Probability distribution
Log-normal distributions are infinitely divisible, but they are not stable distributions, which can be easily drawn from. If X ∼ N ( μ , σ 2 ) {\displaystyle
Log-normal_distribution
Mathematical function common in physics
Weibull distribution. The stretched exponential is also the characteristic function, basically the Fourier transform, of the Lévy symmetric alpha-stable distribution
Stretched exponential function
Stretched_exponential_function
Type of probability distribution
of the stable distribution family, which includes the normal distribution, the Cauchy distribution, and the Lévy distribution. Outside the stable class
Infinite divisibility (probability)
Infinite_divisibility_(probability)
Algorithm that arranges lists in order
the use of a stable sort, the MSD radix sort algorithm does not (unless stable sorting is desired). In-place MSD radix sort is not stable. It is common
Sorting_algorithm
and number of packages available. These tables compare notable distribution's latest stable release on wide-ranging objective criteria. It does not cover
Comparison of Linux distributions
Comparison_of_Linux_distributions
Continuous probability distribution
}})}}} For m = 0, the ALD is a member of the family of geometric stable distributions with α = 2. It follows that if φ 1 {\displaystyle \varphi _{1}} and
Asymmetric Laplace distribution
Asymmetric_Laplace_distribution
Petersburg paradox Stability (probability) Stable distribution Stable and tempered stable distributions with volatility clustering – financial applications
List_of_statistics_articles
Topic in probability theory and statistics
(always?) these distributions are also stable distributions (see also Discrete-stable distribution). Examples of such univariate distributions are: normal
Relationships among probability distributions
Relationships_among_probability_distributions
Probability distribution in mathematics
_{k\log(p)}(dx)} Other "power-law" distributions Cauchy distribution Lévy distribution Lévy skew alpha-stable distribution Pareto distribution Zipf's law Zipf–Mandelbrot
Zeta_distribution
distribution Poisson distribution Stable distribution Mixture distribution Sum of normally distributed random variables "VoigtDistribution". Wolfram Language
List of convolutions of probability distributions
List_of_convolutions_of_probability_distributions
Thermal electromagnetic radiation
from the opening. Black-body radiation has the unique absolutely stable distribution of radiative intensity that can persist in thermodynamic equilibrium
Black-body_radiation
Linux distribution based on Red Hat Enterprise Linux
AlmaLinux is a free and open source Linux distribution, a community-supported, production-grade enterprise operating system that is binary-compatible with
AlmaLinux
List of software distributions using the Linux kernel
independently developed, x86-64 general-purpose Linux distribution that strives to provide the latest stable versions of most software by following a rolling-release
List_of_Linux_distributions
Family of distributions that generalize the multivariate normal distribution
multivariate probability distributions: Multivariate normal distribution Multivariate t-distribution Symmetric multivariate stable distribution Symmetric multivariate
Elliptical_distribution
Operating system based on the Linux kernel
BETA released in January 1994 and first stable version in June 1996. Users were attracted to Linux distributions as alternatives to MS-DOS compatible operating
Linux_distribution
Subbundle of the tangent bundle
be joined by a path tangent to the distribution. A distribution Δ ⊆ T M {\displaystyle \Delta \subseteq TM} is stable if under any C 2 {\displaystyle C^{2}}
Distribution (differential geometry)
Distribution_(differential_geometry)
Linux distribution with low resource requirements
April 2025. "CrunchBang++ Linux – The Ultimate Lightweight and Stable Linux Distribution". CrunchBang Linux. April 2022. Retrieved 30 May 2024. "[ANN]
Comparison of lightweight Linux distributions
Comparison_of_lightweight_Linux_distributions
Feature observed in spectroscopy
Because there are many sources of broadening, the lines have a stable distribution, tending towards a Gaussian shape. The shape of lines in a nuclear
Spectral_line_shape
Aspect of probability theory
Algebra of random variables Stable distribution Standard error (statistics) Ratio distribution Product distribution Slash distribution List of convolutions of
Sum of normally distributed random variables
Sum_of_normally_distributed_random_variables
Nuclide that does not undergo radioactive decay
Stable nuclides are isotopes of a chemical element whose nucleons are in a configuration that does not permit them the surplus energy required to produce
Stable_nuclide
Degree of variation of a trading price series over time
looked at cotton prices and found that they followed a Lévy alpha-stable distribution with α = 1.7. (See New Scientist, 19 April 1997.) Much research has
Volatility_(finance)
Distinctive narrow spectral feature of chemical species
broadening is a 4-parameter generalization of the Gaussian distribution known as a stable distribution. Pressure broadening may also be classified by the nature
Spectral_line
group G in terms of stable distributions. However these stable distributions are not distributions on the group G, but are distributions on a family of quasisplit
Arthur–Selberg_trace_formula
Concept in philosophy and mathematics
are the normal distribution, Cauchy distribution and all other members of the stable distribution family. The skew-normal distribution is an example of
Infinite_divisibility
Fourier transform of the probability density function
probability distributions to samples of data. Cases where this provides a practicable option compared to other possibilities include fitting the stable distribution
Characteristic function (probability theory)
Characteristic_function_(probability_theory)
Medical condition
in size proportionally with the growth of the body, but their distribution remains stable, and they are non-progressive hypopigmented patches. The exact
Nevus_depigmentosus
Second theorem in extreme value theory
distributions, still continuous distributions exist that are not covered. Stable distribution Iii, James Pickands (1975-01-01). "Statistical Inference Using Extreme
Pickands–Balkema–De Haan theorem
Pickands–Balkema–De_Haan_theorem
Type of stochastic process in probability
|/(2\pi ))}.} The marginal probability distribution of the asymmetric Cauchy process is a stable distribution with index of stability (i.e., α parameter)
Cauchy_process
Pore-forming membrane protein
the stable distribution matrix by solving the equation PX=X, where P is the stochastic matrix and X is the stable distribution matrix. This stable distribution
Ion_channel
Stages in development and support of computer software
without establishing a final "stable" release. As the Internet has facilitated the rapid and inexpensive distribution of software, companies have begun
Software_release_life_cycle
Probability distribution
divisible distributions are a fortiori decomposable; in particular, this includes the stable distributions, such as the normal distribution. The uniform
Indecomposable_distribution
Measure of linear correlation
the maximum likelihood estimator. Some distributions (e.g., stable distributions other than a normal distribution) do not have a defined variance. The values
Pearson correlation coefficient
Pearson_correlation_coefficient
Overview of the steel industry of Bangladesh
captive billet manufacturing plants in 1996 so as to make sure a stable distribution of billets of its plants. In 2006, the company installed pilot cold
Steel_industry_in_Bangladesh
Extensions of the concept of randomness
are extensions of the concept of randomness as modeled by the normal distribution. These seven states were first introduced by Benoît Mandelbrot in his
Seven_states_of_randomness
Distribution of a country's total GDP amongst its population
In economics, income distribution covers how a country's total GDP is distributed amongst its population. Economic theory and economic policy have long
Income_distribution
Probability distribution
Since the Cauchy distribution is a stable distribution, the log-Cauchy distribution is a logstable distribution. Logstable distributions have poles at x=0
Log-Cauchy_distribution
Concept in chromatography
or MRF (Multispot Response Function). Besides its stable range, the advantage is a stable distribution as a random variable, regardless of compounds investigated
Retention_distance
Suite of system components for Linux
It has been praised by developers and users of distributions that adopted it for providing a stable, fast out-of-the-box solution for issues that had
Systemd
Features that do not change if length or energy scales are multiplied by a common factor
distributions like the compound Poisson-gamma distribution, positive stable distributions, and extreme stable distributions. Consequent to their inherent scale
Scale_invariance
Indian Debian-based Linux distribution
also referred to as BOSS Linux, is an Indian Linux distribution based on Debian. The latest stable release is 10.0 (Pragya), which was released in March-2024
Bharat Operating System Solutions
Bharat_Operating_System_Solutions
Linux distribution
and MEPIS LLC. The most popular MEPIS distribution was SimplyMEPIS, which was based primarily on Debian stable, with the last version of SimplyMEPIS being
MEPIS
Branch of geometry
called Darboux coordinates. In this sense, contact geometry is a stable distribution, since they are all the same up to local diffeomorphism. α {\displaystyle
Contact_geometry
This is a list of router and firewall distributions, which are operating systems designed for use as routers and/or firewalls. List of open-source routing
List of router and firewall distributions
List_of_router_and_firewall_distributions
Linux distribution
I don't think I ran into any errors while I was using it. The distribution was stable, it worked well with my hardware, and I didn't run into a single
NixOS
Probability distribution
^{2}t^{2}/2-\gamma |t|}.} Since normal distributions and Cauchy distributions are stable distributions, they are each closed under convolution (up
Voigt_profile
Spread of wealth in a society
economic heterogeneity. The distribution of wealth differs from the income distribution in that it looks at the economic distribution of ownership of the assets
Distribution_of_wealth
Stochastic process in probability theory
divisible distributions. Cambridge University Press. pp. 31–68. ISBN 9780521553025. Zolotarev, Vladimir M. One-dimensional stable distributions. Vol. 65
Lévy_process
Application of mathematical and statistical methods in finance
in prices do not follow a Gaussian distribution, but are rather modeled better by Lévy alpha-stable distributions. The scale of change, or volatility
Mathematical_finance
index) or Sm (informational entropy). Besides its stable range, the advantage is a stable distribution as a random variable, regardless of compounds investigated
Retention_uniformity
Statistical transformation
problem by yielding a variable whose distribution is approximately normally distributed, with a variance that is stable over different values of r. Given
Fisher_transformation
Solution concept in game theory
An evolutionarily stable strategy (ESS) is a strategy (or set of strategies) that is impermeable when adopted by a population in adaptation to a specific
Evolutionarily stable strategy
Evolutionarily_stable_strategy
Species distribution of Canis lupus
Wolf distribution is the species distribution of the wolf (Canis lupus). Originally, wolves occurred in Eurasia above the 12th parallel north and in North
Wolf_distribution
German economist (born 1954)
normal distribution to financial returns and had pointed to stable distributions as an alternative framework. His publications have addressed stable distributions
Stefan_Mittnik
following a path whose length is distributed over an inverse square Levy stable distribution, is optimal for searching sparsely and randomly distributed revisitable
Lévy flight foraging hypothesis
Lévy_flight_foraging_hypothesis
Metric for evaluating open-ended text generation
large sample size (often more than 1000 generations) to provide a stable distributional estimate. It is also computationally expensive as it requires running
MAUVE_(metric)
Linux distribution by Fedora Project
is a copy of a complete Fedora distribution where new software is added and tested, before inclusion in a later stable release. As such, Rawhide is often
Fedora_Linux
Geographical area in which a species can be found
Species distribution, or species dispersion, is the manner in which a biological taxon is spatially arranged. The geographic limits of a particular taxon's
Species_distribution
a power-law repulse function was studied and observed to have a stable distribution. Independently, researchers successfully developed Fourier and Laplace
Stochastic geometry models of wireless networks
Stochastic_geometry_models_of_wireless_networks
Lightweight Linux distribution
SliTaz GNU/Linux is a lightweight Linux distribution, community-based, suitable for use on older hardware and as a Live CD or Live USB. SliTaz stands for
SliTaz
Modelling financial risks
financial markets do not follow a Gaussian distribution, but are rather modeled better by Lévy stable distributions. The scale of change, or volatility, depends
Financial_risk_modeling
Generic term for all markets in which trading takes place with capital
changes in prices do not follow a normal distribution, but are rather modeled better by Lévy stable distributions. The scale of change, or volatility, depends
Financial_market
STABLE DISTRIBUTION
STABLE DISTRIBUTION
Surname or Lastname
English
English : occupational name for someone who looked after horses or cattle, from an agent derivative of Middle English stable ‘stable’.German (Stäbler) : occupational name for an official who carried a staff as a symbol of office, Middle High German stebelære.
Surname or Lastname
English (Durham)
English (Durham) : unexplained
Surname or Lastname
English
English : topographic name for someone who lived near a boundary post, from Middle English stapel ‘post’ + the suffix -er, denoting an inhabitant.
Boy/Male
Indian, Punjabi, Sikh
Stable
Surname or Lastname
English
English : topographic name for someone who lived by a stable, or an occupational name for someone employed in one, from Middle English stable, plural stables (via Old French from Latin stabulum, a derivative of stare ‘to stand’). In Middle English the term was used of the quarters occupied by cattle as well as those reserved for horses.
Surname or Lastname
English
English : variant of Staple.
Surname or Lastname
English
English : from Middle English stapel ‘post’, hence a topographic name for someone who lived near a boundary post, or a habitational name from some place named with this word (Old English stapel), as for example Staple in Kent or Staple Fitzpaine in Somerset.Americanized spelling of German Stapel.
Boy/Male
Hindu
Stable
Female
English
Feminine variant spelling of English unisex Stacey, STACEE means "resurrection."
Male
French
French name derived from Latin amabilis, AMABLE means "lovable."
Boy/Male
Vietnamese
Stable.
Surname or Lastname
English (Devon and Cornwall)
English (Devon and Cornwall) : habitational name from Scoble in Devon.
Surname or Lastname
English, Dutch, North German, and Danish
English, Dutch, North German, and Danish : variant of Stubbe.
Female
English
Variant spelling of English Mabel, MABLE means "lovable."Â
Boy/Male
Tamil
Stable
Boy/Male
Shakespearean American English
Henry VI, Part 2' Sir John Stanley. 'King Henry the Sixth, Part III' Sir William Stanley. 'King...
Female
English
Feminine variant spelling of English unisex Stacey, STACIE means "resurrection."
Female
English
English name derived from the vocabulary word, SABLE means "black," as a heraldic color. It is sometimes confused with the mammal of the same name but which has brown fur, not black, and which has a different origin.
Boy/Male
Indian, Sanskrit
Stable
Female
English
Elaborated form of English Star, STARLA means "star."
STABLE DISTRIBUTION
STABLE DISTRIBUTION
Boy/Male
Hindu
Feet pad of Lord Vishnu
Girl/Female
Irish
Olive.
Female
Hebrew
(לִיבָּ×) Variant spelling of Hebrew Liba, LEEBA means "heart." Compare with another form of Leeba.
Girl/Female
American, British, English, Latin
Youthful; Jove's Child; Variant of Gillian from the Masculine Julian
Male
Hindi/Indian
(नीरव) Hindi name NIRAV means "calm, quiet."
Girl/Female
Tamil
Person who knows future, Oracle, Bhagyavidhata
Boy/Male
Arabic, Australian, Muslim
Wire
Female
English
Feminine diminutive form of English unisex Page, PAGET means "little patrician; little servant."
Girl/Female
Dutch
Rules the home.
Boy/Male
Anglo Saxon
Terror.
STABLE DISTRIBUTION
STABLE DISTRIBUTION
STABLE DISTRIBUTION
STABLE DISTRIBUTION
STABLE DISTRIBUTION
n.
A stable keeper.
a.
Pertaining to, or being market of staple for, commodities; as, a staple town.
a.
Liable to, or subjected by law to, taxation; as, ratable estate.
a.
Not stable; not standing fast or firm; unstable; prone to change or recede from a purpose; mutable; inconstant.
imp. & p. p.
of Stable
adv.
In a stable manner; firmly; fixedly; steadily; as, a government stably settled.
v. t.
To put or keep in a stable.
v. i.
Steady in purpose; constant; firm in resolution; not easily diverted from a purpose; not fickle or wavering; as, a man of stable character.
imp. & p. p.
of Sable
n.
The fiber of wool, cotton, flax, or the like; as, a coarse staple; a fine staple; a long or short staple.
v. t.
To form into a table or catalogue; to tabulate; as, to table fines.
v. i.
Firmly established; not easily moved, shaken, or overthrown; fixed; as, a stable government.
v. t.
To sort according to its staple; as, to staple cotton.
v. i.
Durable; not subject to overthrow or change; firm; as, a stable foundation; a stable position.
v. i.
To dwell or lodge in a stable; to dwell in an inclosed place; to kennel.
imp. & p. p.
of Stale
v. i.
A house, shed, or building, for beasts to lodge and feed in; esp., a building or apartment with stalls, for horses; as, a horse stable; a cow stable.
a.
Being of reasonable or suitable size; as, sizable timber; sizable bulk.
n.
The company assembled round a table.
n.
The fur of the sable.