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List of probability topics
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{{Short description|none}} {{ProbabilityTopicsTOC}} 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 (disambiguation)|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 problem]]s * [[Extractor (mathematics)|Extractor]] * [[Free probability]] * [[Exotic probability]] * [[Schrödinger method]] * [[Empirical measure]] * [[GlivenkoâCantelli theorem]] * [[Zeroâone law (disambiguation)|Zeroâone law]] ** [[Kolmogorov's zeroâone law]] ** [[HewittâSavage zeroâone law]] * [[Law of truly large numbers]] ** [[Littlewood's law]] ** [[Infinite monkey theorem]] * [[LittlewoodâOfford problem]] * [[Inclusionâexclusion 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 (probability)|Bertrand's paradox]] * [[Coherence (philosophical gambling strategy)]] * [[Dutch book]] * [[Algebra of random variables]] * [[Belief propagation]] * [[Transferable belief model]] * [[DempsterâShafer theory]] * [[Possibility theory]] ==[[Random variable]]s== * [[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]] *** [[HellyâBray theorem]] *** [[Slutsky's theorem]] ** [[Skorokhod's representation theorem]] ** [[LĂ©vy'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]] * [[ChungâErdĆs inequality]] * [[Khintchine inequality]] * [[PaleyâZygmund inequality]] * [[Laws of large numbers]] ** [[Asymptotic equipartition property]] ** [[Typical set]] ** [[Law of large numbers]] ** [[Kolmogorov's two-series theorem]] * [[Random field]] ** [[Conditional random field]] * [[BorelâCantelli 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]] ** [[GoodmanâNguyenâvan Fraassen algebra]] ==Theory of probability distributions== * [[Probability distribution]] * [[Probability density function|Probability distribution function]] * [[Probability density function]] * [[Probability mass function]] * [[Cumulative distribution function]] * [[Quantile]] * [[Moment (mathematics)]] ** [[Moment about the mean]] ** [[Standardized moment]] *** [[Skewness]] *** [[Kurtosis]] *** [[Locality (statistics)|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|Total variation distance]] * [[Hellinger distance]] * [[Wasserstein metric]] * [[LĂ©vyâProkhorov metric]] ** [[LĂ©vy 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]] ** [[BerryâEsseen theorem|BerryâEssĂ©en theorem]] ** [[BerryâEssĂ©en theorem]] ** [[De MoivreâLaplace 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)]] ** [[LĂ©vy continuity theorem]] * [[DarmoisâSkitovich theorem]] * [[Edgeworth series]] * [[HellyâBray theorem]] * [[KacâBernstein theorem]] * [[Location parameter]] * [[Maxwell's theorem]] * [[Moment-generating function]] ** [[Factorial moment generating function]] * [[Negative probability]] * [[Probability-generating function]] * [[VysochanskiĂŻâPetunin inequality]] * [[Mutual information]] * [[KullbackâLeibler 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]] ** [[CramĂ©r's theorem (large deviations)|CramĂ©r's theorem]] (second part) ==[[Applied probability]]== * ''Empirical findings'' ** [[Benford's law]] ** [[Pareto principle]] ** [[Zipf's law]] *[[Boy or Girl paradox]] ==[[Stochastic process]]es== * [[Adapted process]] * [[Basic affine jump diffusion]] * [[Bernoulli process]] ** [[Bernoulli scheme]] * [[Branching process]] * [[Point process]] * [[ChapmanâKolmogorov equation]] * [[Chinese restaurant process]] * [[Coupling (probability)]] * [[Ergodic theory]] ** [[Maximal ergodic theorem]] ** [[Ergodic (adjective)]] * [[GaltonâWatson process]] * [[GaussâMarkov process]] * [[Gaussian process]] ** [[Gaussian random field]] ** [[Gaussian isoperimetric inequality]] ** [[Large deviations of Gaussian random functions]] * [[Girsanov's theorem]] * [[Hawkes process]] * [[Increasing process]] * [[ItĂŽ's lemma]] * [[Jump diffusion]] * [[Law of the iterated logarithm]] * [[LĂ©vy flight]] * [[LĂ©vy 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 (probability theory)|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]] ** [[ItĂŽ 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)]] ** [[Charles Wells (gambler)|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]] * [[BoxâMuller 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 (finance)|Volatility]] * [[SWOT analysis#Marketing|SWOT analysis (Marketing)]] * [[Kelly criterion]] ==[[Genetics]]== * [[Punnett square]] * [[HardyâWeinberg principle]] * [[Ewens's sampling formula]] * [[Population genetics]] ==Historical== * [[History of probability]] * ''[[The Doctrine of Chances]]'' {{DEFAULTSORT:Probability}} [[Category:Probability|*]] [[Category:Statistics-related lists]] [[Category:Lists of topics]]
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