List of probability topics
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This is a list of probability topics, by Wikipedia page. 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 generator
- 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
- Aleatoric, aleatoric music
- 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–Offord problem
- Inclusion-exclusion principle
- Impossible event
- Information geometry
- Talagrand's concentration inequality
Foundations of probability theory
- Probability theory
- Probability space
- Probability axioms
- Normalizing constant
- Event (probability theory)
- 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
- Constant random variable
- Expected value
- Variance
- Multivariate random variable
- Independent identically-distributed random variables
- Independent and identically-distributed random variables
- Statistical independence
- Correlation
- Canonical correlation
- Convergence of random variables
- Weak convergence of measures
- 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)
- Kolmogorov's inequality
- Etemadi's inequality
- Khintchine inequality
- Paley–Zygmund inequality
- Laws of large numbers
- 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
- Rule of succession
- Conditional independence
- Conditional event 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
- Cumulant
- Factorial moment
- Expected value
- 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
- Prior probability distribution
- Total variation distance
- Hellinger distance
- Wasserstein metric
- Lévy–Prokhorov 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
- Martingale central limit theorem
- Infinite divisibility (probability)
- Method of moments (probability theory)
- Stability (probability)
- Stein's lemma
- Characteristic function (probability theory)
- Lévy continuity theorem
- Edgeworth series
- Helly–Bray theorem
- Location parameter
- Maxwell's theorem
- Moment-generating function
- Negative probability
- Probability-generating function
- Vysochanskiï–Petunin inequality
- Mutual information
- Kullback–Leibler divergence
- Normally distributed and uncorrelated does not imply independent
- Le Cam's theorem
- Large deviations theory
Applied probability
- Empirical findings
Stochastic processes
- Adapted process
- Basic affine jump diffusion
- Bernoulli process
- 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
- Girsanov's theorem
- Increasing process
- Itô's lemma
- Jump diffusion
- Law of the iterated logarithm
- Lévy flight
- Lévy process
- Loop-erased random walk
- Markov chain
- Markov partition
- Markov process
- Continuous-time Markov process
- Piecewise-deterministic Markov process
- Martingale
- Poisson process
- 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
Geometric probability
Gambling
- Luck
- Game of chance
- Odds
- Gambler's fallacy
- Inverse gambler's fallacy
- Parrondo's paradox
- Pascal's wager
- Gambler's ruin
- Poker probability
- Roulette
- Martingale (betting system)
- The man who broke the bank at Monte Carlo
- Lottery
- Coherence (philosophical gambling strategy)
- Coupon collector's problem
Coincidence
- Birthday paradox
- 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