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When the linear combination of a random variable with itself has the same distribution
In probability theory, the stability of a random variable is the property that a linear combination of two independent copies of the variable has the
Stability_(probability)
Stability of soil or rock slopes
the probability of a slope movement. A previously stable slope can be affected by a number of predisposing factors or processes that reduce stability -
Slope_stability
Topics referred to by the same term
stability Exponential stability Linear stability Lyapunov stability Marginal stability Orbital stability Structural stability Stability (probability)
Stability
Distribution of variables which satisfies a stability property under linear combinations
In probability theory, a distribution is said to be stable if a linear combination of two independent random variables with this distribution has the
Stable_distribution
Smoothly functioning political system
upholding the rule of law. Societies with political stability experience a decreased probability of encountering major political upheavals, civil unrest
Political_stability
In probability theory, to obtain a nondegenerate limiting distribution for extremes of samples, it is necessary to "reduce" the actual greatest value
Stability_postulate
Family of probability distributions
In probability theory and statistics, the generalized extreme value (GEV) distribution is a family of continuous probability distributions developed within
Generalized extreme value distribution
Generalized_extreme_value_distribution
divisibility (probability) Method of moments (probability theory) Stability (probability) Stein's lemma Characteristic function (probability theory) Lévy
List_of_probability_topics
Ability to manage financial crisis
empirical research as a measure of firm-level stability for its high correlation with the probability of default. This measure contrasts buffers (capitalization
Financial_stability
Prediction in nuclear physics
In nuclear physics, the island of stability is a predicted set of isotopes of superheavy elements that may have considerably longer half-lives than known
Island_of_stability
Discrete probability distribution
probability theory and statistics, the Poisson distribution (US: /pwɑːˈsɒn/ pwahss-ON, UK: /ˈpwɑːsɒn, ˈpwæsɒn/ PWA(H)SS-on) is a discrete probability
Poisson_distribution
sliding criterion is part of the Slope Stability Probability Classification (SSPC) system for slope stability analyses. The sliding-angle is calculated
Sliding criterion (geotechnical engineering)
Sliding_criterion_(geotechnical_engineering)
International relations theory
countries each have nuclear weapons, the probability of a direct war between them greatly decreases, but the probability of minor or indirect conflicts between
Stability–instability_paradox
Written work by John Maynard Keynes
A Treatise on Probability, published by John Maynard Keynes in 1921, provides a much more general logic of uncertainty than the more familiar and straightforward
A_Treatise_on_Probability
Random process independent of past history
In probability theory and statistics, a Markov chain or Markov process is a stochastic process describing a sequence of possible events in which the probability
Markov_chain
Effect of variables' uncertainties on the uncertainty of a function based on them
analysis Interval finite element Measurement uncertainty Numerical stability Probability bounds analysis Uncertainty quantification Random-fuzzy variable
Propagation_of_uncertainty
Computerized safety automotive technology
Electronic stability control (ESC), also referred to as electronic stability program (ESP) or dynamic stability control (DSC), is a computerized technology
Electronic_stability_control
French polymath (1749–1827)
mechanics and the stability of the Solar System. The two disciplines would always be interlinked in his mind. "Laplace took probability as an instrument
Pierre-Simon_Laplace
root biased sampling Squared deviations St. Petersburg paradox Stability (probability) Stable distribution Stable and tempered stable distributions with
List_of_statistics_articles
Topics referred to by the same term
Scottish School of Primary Care, an academic institution Slope Stability Probability Classification, a classification system for slope engineering Society
SSPC
Croatian–American mathematician
Gillespie algorithm Kolmogorov equations Poisson point process Stability (probability) St. Petersburg paradox Stochastic process Zubrinic, Darko (2006)
William_Feller
Surface dividing a soil or rock mass by differing properties
(10): 257–273. ISSN 0038-223X. Hack, H.R.G.K. (1998) [1996]. Slope Stability Probability Classification (SSPC) (PDF). ITC publication 43. Technical University
Discontinuity (geotechnical engineering)
Discontinuity_(geotechnical_engineering)
Image-generating machine learning model
diffusion techniques. The generative AI technology is the premier product of Stability AI and is considered to be a part of the ongoing AI boom. It is primarily
Stable_Diffusion
Russian mathematician (1857–1918)
development of the stability theory of a dynamical system, as well as for his many contributions to mathematical physics and probability theory. Lyapunov
Aleksandr_Lyapunov
Probability has a dual aspect: on the one hand the likelihood of hypotheses given the evidence for them, and on the other hand the behavior of stochastic
History_of_probability
Measure of algorithm accuracy
where ρ(x→,y) is the unknown joint probability distribution for x→ and y. Without knowing the joint probability distribution ρ, it is impossible to compute
Generalization_error
Mass Rating Rock mass classification system for rock slopes Slope Stability Probability Classification (SSPC) Q-slope Rock load classification method The
Rock_mass_classification
Collection of random variables
In probability theory and related fields a stochastic (/stəˈkæstɪk/) or random process is a mathematical object usually defined as a family of random
Stochastic_process
Terms used to convey the likelihood of an event occurring
Words of estimative probability (WEP or WEPs) are terms used by intelligence analysts in the production of analytic reports to convey the likelihood of
Words of estimative probability
Words_of_estimative_probability
Logarithm of probabilities, useful for calculations
In probability theory and computer science, a log probability is simply a logarithm of a probability. The use of log probabilities means representing
Log_probability
Financial term
Probability of default (PD) is a financial term describing the likelihood of a default over a particular time horizon. It provides an estimate of the
Probability_of_default
When an ecosystem does not drastically change over time even after perturbation
Although the terms community stability and ecological stability are sometimes used interchangeably, community stability refers only to the characteristics
Ecological_stability
Mathematical statistics distance measure
distance: a measure of how much an approximating probability distribution Q is different from a true probability distribution P. Mathematically, it is defined
Kullback–Leibler_divergence
American mathematician
Maury; Durrett, Rick (1988). "A simple proof of the stability criterion of Gray and Griffeath". Probability Theory and Related Fields. 80 (2): 293–298. doi:10
Maury_Bramson
Lithuanian mathematician
Lithuanian mathematician who worked in probability theory and characterization of probability distributions and its stability. He was a professor at the Lithuanian
Romanas_Januškevičius
Smooth approximation of one-hot arg max
normalized exponential function, converts a tuple of K real numbers into a probability distribution over K possible outcomes. It is a generalization of the
Softmax_function
Professor of operations research at MIT
Technology's Sloan School of Management. His research spans discrete probability, statistics and machine learning, algorithms and optimization, quantum
David_Gamarnik
Topics referred to by the same term
Lyapunov theorem may refer to: Lyapunov theory, a theorem related to the stability of solutions of differential equations near a point of equilibrium Lyapunov
Lyapunov_theorem
Long term dynamical interactions that disrupt the Solar System
The stability of the Solar System is a subject of much inquiry in astronomy. Though the planets have historically been stable as observed, and will be
Stability_of_the_Solar_System
Purely statistical model of language
language model is a statistical model of language which calculates the probability of the next word in a sequence from a fixed size window of previous words
Word_n-gram_language_model
which the problems of this kind are considered are called stability characterizations of probability distributions. Characterization (mathematics) V.M. Zolotarev
Characterization of probability distributions
Characterization_of_probability_distributions
Study of Boolean functions via discrete Fourier analysis
formula gives the asymptotic noise stability of majority: Stabρ[Majn]⟶1−2πarccosρ. This is related to the probability that if we choose x∈{−1,1}n uniformly
Analysis_of_Boolean_functions
Theory of behavioral economics
if its probability were 95%, and an outcome with probability of 1% as if it had a probability of 5%. Under- and over-weighting of probabilities is importantly
Prospect_theory
Strategic stability is a concept in international relations indicating a lack of incentives for any party to initiate the nuclear first strike; the term
Strategic_stability
French mathematician and historian (1822–1900)
science whose work emphasized number theory, differential geometry, probability theory, economics and thermodynamics. He lends his name to various paradoxes
Joseph_Bertrand
Fundamental theorem in probability theory and statistics
In probability theory, the central limit theorem (CLT) states that, under appropriate conditions, the distribution of a normalized version of the sample
Central_limit_theorem
Probability of existentially catastrophic outcomes in AI
In the AI safety field, P(doom) is the probability of existentially catastrophic outcomes (so-called "doomsday scenarios") as a result of artificial intelligence
P(doom)
Probability distribution
In probability theory, a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally
Log-normal_distribution
Framework for machine learning
uniqueness, and stability of the solution. Consider a binary classifier f:𝒳→{0,1}. We can apply Hoeffding's inequality to bound the probability that the empirical
Statistical_learning_theory
In probability theory, Foster's theorem, named after Gordon Foster, is used to draw conclusions about the positive recurrence of Markov chains with countable
Foster's_theorem
Rate-seeking algorithm
possibilities for delay increases exponentially. This decreases the probability of a collision but increases the average latency. Exponential backoff
Exponential_backoff
Science of characterizing uncertainties
traditional (frequentist) probability is the most basic form. Techniques such as the Monte Carlo method are frequently used. A probability distribution can be
Uncertainty_quantification
Expected value of a random variable given that certain conditions are known to occur
In probability theory, the conditional expectation, conditional expected value, or conditional mean of a random variable is its expected value evaluated
Conditional_expectation
Intermediate energetic state within a dynamical system
Indeed, above absolute zero, all states of a system have a non-zero probability to decay; that is, to spontaneously fall into another state (usually
Metastability
Probability distribution in physics
a continuous probability distribution. The Holtsmark distribution is a special case of a stable distribution with the index of stability or shape parameter
Holtsmark_distribution
System to maintain vehicle trajectory in lieu of direct operator command
(660 ft). It needs a fail-passive autopilot. There must be only a 10−6 probability of landing outside the prescribed area. CAT IIIb – As IIIa but with the
Autopilot
Semiring defined over probabilities
types (for probabilities or log-probabilities) combined with appropriate operations. The key consideration is numerical stability: probabilities multiplied
Viterbi_semiring
(probability theory) Dirichlet-multinomial distribution Dirichlet negative multinomial distribution Generalized Dirichlet distribution (probability theory)
List of things named after Peter Gustav Lejeune Dirichlet
List_of_things_named_after_Peter_Gustav_Lejeune_Dirichlet
Method for analyzing stability of slopes of soil or rock
failure and the probability of failure (both require an understanding of the failure mechanism). Conventional methods of slope stability analysis can be
Slope_stability_analysis
Load measure in telecommunications
the probability of this occurring. In contrast, the Erlang C formula provides for the possibility of an unlimited queue and it gives the probability that
Erlang_(unit)
Calculation of complex statistical distributions
is a class of algorithms used to draw samples from a probability distribution. Given a probability distribution, one can construct a Markov chain whose
Markov_chain_Monte_Carlo
Measurement related to thunderstorms
{\displaystyle T_{500}} = Temperature at 500 hPa The K Index is related to the probability of occurrence of a thunderstorm. It was developed with the idea that
K-index_(meteorology)
Russian mathematician (1931–2026)
heavy traffic approximations Ergodicity and stability of stochastic systems Limit theorems in probability theory These works are frequently cited in the
Aleksandr_Borovkov
Effect that limits performance of advanced atomic clocks
referred to as "the effect") is an important limitation to frequency stability for modern atomic clocks such as atomic fountains and optical lattice
Dick_effect
Probabilistic problem-solving algorithm
generating draws from a sequence of probability distributions satisfying a nonlinear evolution equation. These flows of probability distributions can always be
Monte_Carlo_method
Ensemble of states at a constant temperature
principal thermodynamic variable of the canonical ensemble, determining the probability distribution of states, is the absolute temperature (symbol: T). The
Canonical_ensemble
Self-exciting counting process
Pierre; Massoulié, Laurent (1 July 1996). "Stability of nonlinear Hawkes processes". The Annals of Probability. 24 (3). doi:10.1214/aop/1065725193. Reynaud-Bouret
Hawkes_process
Inc.) Joel Marks; cast: Thomas E. Cronin c-16m 1990 Modern President Probability and Its Uses Evan M. Maletsky c-14m April 21, 1973 Propaganda Techniques
List_of_Coronet_Films_films
Model-free reinforcement learning algorithm
probability distribution P(A|S) generated by the policy network. The actions that are most likely to be beneficial will have the highest probability of
Proximal_policy_optimization
Branch of engineering and mathematics
delay, overshoot, or steady-state error and ensuring a level of control stability; often with the aim to achieve a degree of optimality. To do this, a controller
Control_theory
Extra-dimensional model of the universe
spacetime that is only warped along the fifth dimension, the graviton's probability function is extremely high at the Planckbrane, but it drops exponentially
Randall–Sundrum_model
Russian mathematician (1937–2023)
Khasminskii, R. Z. (2012). Stochastic Stability of Differential Equations. Stochastic Modelling and Applied Probability. Vol. 66. Springer. doi:10.1007/978-3-642-23280-0
Grigori_Milstein
States of matter for water as a solid
hydrogen atom. Assuming that the lattice edges are independent, then the probability that a single edge contains exactly one hydrogen atom is 1/2, and since
Phases_of_ice
Application of mathematical and statistical methods in finance
different probabilities such as the risk-neutral probability (or arbitrage-pricing probability), denoted by "Q", and the actual (or actuarial) probability, denoted
Mathematical_finance
Twenty-first letter in the Greek alphabet
homomorphisms In probability theory, φ(x)=(2π)−12e−x22 is the probability density function of the standard normal distribution. In probability theory, φX(t)
Phi
Statistical Markov model
In probability theory, a hidden Markov model (HMM) is a Markov model in which the observations are dependent on a latent (or hidden) Markov process (referred
Hidden_Markov_model
Method of statistical inference
calculates the conditional probability of observing a value at least this extreme, supposing the null hypothesis is true. If this probability (called the p-value)
Statistical_hypothesis_test
1713 book on probability and combinatorics by Jacob Bernoulli
"The Art of Conjecturing") is a book on combinatorics and mathematical probability written by Jacob Bernoulli and published in 1713, eight years after his
Ars_Conjectandi
Wiener process with reflecting spatial boundaries
In probability theory, reflected Brownian motion (or regulated Brownian motion, both with the acronym RBM) is a Wiener process in a space with reflecting
Reflected_Brownian_motion
Description of physical properties at the atomic and subatomic scale
gives probabilities. Mathematically, a probability is found by taking the square of the absolute value of a complex number, known as a probability amplitude
Quantum_mechanics
Theory of response to surprise events
non-computability of the probability of consequential rare events using scientific methods (owing to the very nature of small probabilities). The individual and
Black_swan_theory
Solution concept of a non-cooperative game
strategies, where players choose a probability distribution over possible pure strategies (which might put 100% of the probability on one pure strategy; such
Nash_equilibrium
Peace due to nuclear deterrence
due to the probability of MAD. The phrase Pax Atomica is derived from the more popular term Pax Romana, which describes the period of stability under Roman
Pax_Atomica
Material property
Francis. p. 536. ISBN 978-0-419-16030-4. Hack, R. (1998). Slope Stability Probability Classification (SSPC) (PDF). ITC publication 43 (2nd ed.). Technical
Shear strength (discontinuity)
Shear_strength_(discontinuity)
Discrete set of Boolean variables
its truth table, whose outputs are randomly populated. pi denotes the probability of assigning an off output to a given series of input signals. If pi=p=const
Boolean_network
Electronic Journal of Probability. 18. arXiv:1110.3813. doi:10.1214/EJP.v18-1958. S2CID 1453859. Costa, O. L. V.; Dufour, F. (2008). "Stability and Ergodicity
Piecewise-deterministic Markov process
Piecewise-deterministic_Markov_process
Probability and computer science concept
In probability theory and theoretical computer science, McDiarmid's inequality (named after Colin McDiarmid ) is a concentration inequality which bounds
McDiarmid's_inequality
Quantum mechanics principle
principle underpins many properties of everyday matter, from its large-scale stability to the chemical behavior of atoms. Half-integer spin means that the intrinsic
Pauli_exclusion_principle
Solution concept for non-cooperative games
theory, Mertens stability is a solution concept used to predict the outcome of a non-cooperative game. A tentative definition of stability was proposed by
Mertens-stable_equilibrium
lists articles related to probability theory. In particular, it lists many articles corresponding to specific probability distributions. Such articles
Catalog of articles in probability theory
Catalog_of_articles_in_probability_theory
Measure of frequency stability in clocks and oscillators
(AVAR), also known as two-sample variance, is a measure of frequency stability in clocks, oscillators and amplifiers. It is named after David W. Allan
Allan_variance
Probability distribution
In probability theory, the Landau distribution is a probability distribution named after Lev Landau who used it in 1944. Because of the distribution's
Landau_distribution
Chemical element with atomic number 117 (Ts)
pair of a target and a beam is characterized by its cross section—the probability that fusion will occur if two nuclei approach one another expressed in
Tennessine
Enzyme
amino acids like tyrosine, phenylalanine and tryptophan increase the probability of cleavage. The zymogen pepsinogen is secreted by the gastric chief
Pepsin
state S is also stochastically stable if under vanishing noise, the probability that the population is in the vicinity of state S does not go to zero
Stochastically stable equilibrium
Stochastically_stable_equilibrium
Machine learning framework
all probability measures μG on Ω. The discriminator's strategy set is the set of Markov kernels μD:Ω→𝒫[0,1], where 𝒫[0,1] is the set of probability measures
Generative adversarial network
Generative_adversarial_network
Lack of quantifiable knowledge in economics
variation is one of the fundamental issues in the philosophy of probability, and different probability interpretations treat predictable and unpredictable variation
Knightian_uncertainty
Measure of distance to normality
negentropy is used as a measure of distance to normality. Out of all probability distributions with a given mean and variance, the Gaussian or normal
Negentropy
Periodic table of the elements with eight or more periods
hypothesized to be within an island of stability that is resistant to fission but not to alpha decay. Other islands of stability beyond the known elements may
Extended_periodic_table
Atoms of different elements with the same number of nucleons
isobar may occur. For instance, radioactive iodine-126 has almost equal probabilities for two decay modes: positron emission, leading to tellurium-126, and
Isobar_(nuclide)
travel, tourism, insurance
STABILITY PROBABILITY
STABILITY PROBABILITY
Boy/Male
Indian, Sanskrit
Poetic; Ability; Intelligence
Biblical
preparation, or stability, of Jehovah
Boy/Male
Arabic, Muslim
Firmness; Stability; Certainty; Endurance; Boldness; Truth
Girl/Female
Hindu, Indian, Marathi
Ability
Girl/Female
Muslim
Stability
Girl/Female
Arabic, Muslim
Stability; Firmness; Certainty; Boldness; Truth; Endurance
Girl/Female
Biblical
Preparation, or stability, of the Lord.
Boy/Male
Arabic
Capacity; Ability
Girl/Female
Hindu
Bravery, Power, Ability
Male
Greek
Short form of Greek Eustathios, STATHIS means "good stability."
Girl/Female
Indian
Stability
Girl/Female
Hindu, Indian, Kannada, Tamil, Telugu
Saint; Yoga; Ability
Male
Chinese
stability and fortune.
Girl/Female
Hindu, Indian
Ability; Capacity
Boy/Male
Arabic, Muslim
Ability; Ingenuity; Intellect; Wit
Boy/Male
Arabic
Fitness; Ability
Boy/Male
Arabic, Muslim
Fitness; Ability
Girl/Female
Hindu, Indian
Ability
Girl/Female
Indian, Marathi
Stability; Discipline; Dedication; Over-cautious; Stubborn.
Girl/Female
Tamil
Vikranti | விகà¯à®°à®¾à®‚தி
Bravery, Power, Ability
STABILITY PROBABILITY
STABILITY PROBABILITY
STABILITY PROBABILITY
STABILITY PROBABILITY
STABILITY PROBABILITY
STABILITY PROBABILITY
STABILITY PROBABILITY
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