javascript is disabled, enable it otherwise the site will not work properly!

javascript est désactivé, activez-le sinon le site ne fonctionnera pas correctement !

List of probability topics

This is a list of probability topics. It overlaps with the (alphabetical) list of statistical topics. There are also the outline of probability and catalog of articles in probability theory. For distributions, see List of probability distributions. For journals, see list of probability journals. For contributors to the field, see list of mathematical probabilists and list of statisticians.

General aspects

Probability
Randomness, Pseudorandomness, Quasirandomness
Randomization, hardware random number generator
Random number generation
Random sequence
Uncertainty
Statistical dispersion
Observational error
Equiprobable
- Equipossible
Average
Probability interpretations
Markovian
Statistical regularity
Central tendency
Bean machine
Relative frequency
Frequency probability
Maximum likelihood
Bayesian probability
Principle of indifference
Credal set
Cox's theorem
Principle of maximum entropy
Information entropy
Urn problems
Extractor
Free probability
Exotic probability
Schrödinger method
Empirical measure
Glivenko–Cantelli theorem
Zero–one law
- Kolmogorov's zero–one law
- Hewitt–Savage zero–one law
Law of truly large numbers
- Littlewood's law
- Infinite monkey theorem
Littlewood–Offord problem
Inclusion–exclusion principle
Impossible event
Information geometry
Talagrand's concentration inequality

Foundations of probability theory

Probability theory
Probability space
- Sample space
- Standard probability space
- Random element
  - Random compact set
- Dynkin system
Probability axioms
Normalizing constant
Event (probability theory)
- Complementary event
Elementary event
Mutually exclusive
Boole's inequality
Probability density function
Cumulative distribution function
Law of total cumulance
Law of total expectation
Law of total probability
Law of total variance
Almost surely
Cox's theorem
Bayesianism
Prior probability
Posterior probability
Borel's paradox
Bertrand's paradox
Coherence (philosophical gambling strategy)
Dutch book
Algebra of random variables
Belief propagation
Transferable belief model
Dempster–Shafer theory
Possibility theory

Random variables

Discrete random variable
- Probability mass function
Constant random variable
Expected value
- Jensen's inequality
Variance
- Standard deviation
- Geometric standard deviation
Multivariate random variable
- Joint probability distribution
- Marginal distribution
- Kirkwood approximation
Independent identically-distributed random variables
- Independent and identically-distributed random variables
Statistical independence
- Conditional independence
- Pairwise independence
- Covariance
- Covariance matrix
- De Finetti's theorem
Correlation
- Uncorrelated
- Correlation function
Canonical correlation
Convergence of random variables
- Weak convergence of measures
  - Helly–Bray theorem
  - Slutsky's theorem
- Skorokhod's representation theorem
- Lévy's continuity theorem
- Uniform integrability
Markov's inequality
Chebyshev's inequality = Chernoff bound
Chernoff's inequality
Bernstein inequalities (probability theory)
- Hoeffding's inequality
Kolmogorov's inequality
Etemadi's inequality
Chung–Erdős inequality
Khintchine inequality
Paley–Zygmund inequality
Laws of large numbers
- Asymptotic equipartition property
- Typical set
- Law of large numbers
- Kolmogorov's two-series theorem
Random field
- Conditional random field
Borel–Cantelli lemma
Wick product

Conditional probability

Conditioning (probability)
Conditional expectation
Conditional probability distribution
Regular conditional probability
Disintegration theorem
Bayes' theorem
de Finetti's theorem
- Exchangeable random variables
Rule of succession
Conditional independence
Conditional event algebra
- Goodman–Nguyen–van Fraassen algebra

Theory of probability distributions

Probability distribution
Probability distribution function
Probability density function
Probability mass function
Cumulative distribution function
Quantile
Moment (mathematics)
- Moment about the mean
- Standardized moment
  - Skewness
  - Kurtosis
  - Locality
- Cumulant
- Factorial moment
- Expected value
  - Law of the unconscious statistician
- Second moment method
- Variance
  - Coefficient of variation
  - Variance-to-mean ratio
- Covariance function
- An inequality on location and scale parameters
- Taylor expansions for the moments of functions of random variables
- Moment problem
  - Hamburger moment problem
    - Carleman's condition
  - Hausdorff moment problem
  - Trigonometric moment problem
  - Stieltjes moment problem
Prior probability distribution
Total variation distance
Hellinger distance
Wasserstein metric
Lévy–Prokhorov metric
- Lévy metric
Continuity correction
Heavy-tailed distribution
Truncated distribution
Infinite divisibility
Stability (probability)
Indecomposable distribution
Power law
Anderson's theorem
Probability bounds analysis
Probability box

Properties of probability distributions

Central limit theorem
- Illustration of the central limit theorem
- Concrete illustration of the central limit theorem
- Berry–Esséen theorem
- Berry–Esséen theorem
- De Moivre–Laplace theorem
- Lyapunov's central limit theorem
- Misconceptions about the normal distribution
- Martingale central limit theorem
- Infinite divisibility (probability)
- Method of moments (probability theory)
- Stability (probability)
- Stein's lemma
Characteristic function (probability theory)
- Lévy continuity theorem
Darmois–Skitovich theorem
Edgeworth series
Helly–Bray theorem
Kac–Bernstein theorem
Location parameter
Maxwell's theorem
Moment-generating function
- Factorial moment generating function
Negative probability
Probability-generating function
Vysochanskiï–Petunin inequality
Mutual information
Kullback–Leibler divergence
Le Cam's theorem
Large deviations theory
- Contraction principle (large deviations theory)
- Varadhan's lemma
- Tilted large deviation principle
- Rate function
- Laplace principle (large deviations theory)
- Exponentially equivalent measures
- Cramér's theorem (second part)

Applied probability

Empirical findings
- Benford's law
- Pareto principle
- Zipf's law
Boy or Girl paradox

Stochastic processes

Adapted process
Basic affine jump diffusion
Bernoulli process
- Bernoulli scheme
Branching process
Point process
Chapman–Kolmogorov equation
Chinese restaurant process
Coupling (probability)
Ergodic theory
- Maximal ergodic theorem
- Ergodic (adjective)
Galton–Watson process
Gauss–Markov process
Gaussian process
- Gaussian random field
- Gaussian isoperimetric inequality
- Large deviations of Gaussian random functions
Girsanov's theorem
Hawkes process
Increasing process
Itô's lemma
Jump diffusion
Law of the iterated logarithm
Lévy flight
Lévy process
Loop-erased random walk
Markov chain
- Examples of Markov chains
- Detailed balance
- Markov property
- Hidden Markov model
- Maximum-entropy Markov model
- Markov chain mixing time
Markov partition
Markov process
- Continuous-time Markov process
- Piecewise-deterministic Markov process
Martingale
- Doob martingale
- Optional stopping theorem
- Martingale representation theorem
- Azuma's inequality
- Wald's equation
Poisson process
- Poisson random measure
Population process
Process with independent increments
Progressively measurable process
Queueing theory
- Erlang unit
Random walk
Random walk Monte Carlo
Renewal theory
Skorokhod's embedding theorem
Stationary process
Stochastic calculus
- Itô calculus
- Malliavin calculus
- Stratonovich integral
Time series analysis
- Autoregressive model
- Moving average model
- Autoregressive moving average model
- Autoregressive integrated moving average model
- Anomaly time series
Voter model
Wiener process
- Brownian motion
- Geometric Brownian motion
- Donsker's theorem
- Empirical process
- Wiener equation
- Wiener sausage

Geometric probability

Buffon's needle
Integral geometry
Hadwiger's theorem
Wendel's theorem

Gambling

Luck
Game of chance
Odds
Gambler's fallacy
Inverse gambler's fallacy
Parrondo's paradox
Pascal's wager
Gambler's ruin
Poker probability
- Poker probability (Omaha)
- Poker probability (Texas hold 'em)
- Pot odds
Roulette
- Martingale (betting system)
- The man who broke the bank at Monte Carlo
Lottery
- Lottery machine
- Pachinko
Coherence (philosophical gambling strategy)
Coupon collector's problem

Coincidence

Birthday paradox
- Birthday problem
Index of coincidence
Bible code
Spurious relationship
Monty Hall problem

Algorithmics

Probable prime
Probabilistic algorithm = Randomised algorithm
Monte Carlo method
Las Vegas algorithm
Probabilistic Turing machine
Stochastic programming
Probabilistically checkable proof
Box–Muller transform
Metropolis algorithm
Gibbs sampling
Inverse transform sampling method
Walk-on-spheres method

Financial mathematics

Risk
Value at risk
Market risk
Risk-neutral measure
Volatility
SWOT analysis (Marketing)
Kelly criterion

Genetics

Punnett square
Hardy–Weinberg principle
Ewens's sampling formula
Population genetics

Historical

History of probability
The Doctrine of Chances

Text submitted to CC-BY-SA license. Source: List of probability topics by Wikipedia (Historical)

Articles connexes

Owlapps.net - since 2012 - Les chouettes applications du hibou