This page lists articles related to probability theory. In particular, it lists many articles corresponding to specific probability distributions. Such articles are marked here by a code of the form (X:Y), which refers to number of random variables involved and the type of the distribution. For example (2:DC) indicates a distribution with two random variables, discrete or continuous. Other codes are just abbreviations for topics. The list of codes can be found in the table of contents.
Random variable Continuous probability distribution / (1:C) Cumulative distribution function / (1:DCR) Discrete probability distribution / (1:D) Independent and identically-distributed random variables / (FS:BDCR) Joint probability distribution / (F:DC) |
Marginal distribution / (2F:DC) Probability density function / (1:C) Probability distribution / (1:DCRG) Probability distribution function Probability mass function / (1:D) Sample space |
Berkson's paradox / (2:B) Bertrand's box paradox / (F:B) Borel–Kolmogorov paradox / cnd (2:CM) Boy or Girl paradox / (2:B) Exchange paradox / (2:D) Monty Hall problem / (F:B) Necktie paradox |
Nontransitive dice Simpson's paradox Sleeping Beauty problem St. Petersburg paradox / mnt (1:D) Three Prisoners problem Two envelopes problem |
Chebyshev's inequality / (1:R) An inequality on location and scale parameters / (1:R) Azuma's inequality / (F:BR) Bennett's inequality / (F:R) Bernstein inequalities / (F:R) Bhatia–Davis inequality Chernoff bound / (F:B) Doob's martingale inequality / (FU:R) Dudley's theorem / Gau Entropy power inequality Etemadi's inequality / (F:R) |
Gauss's inequality Hoeffding's inequality / (F:R) Khintchine inequality / (F:B) Kolmogorov's inequality / (F:R) Marcinkiewicz–Zygmund inequality / mnt Markov's inequality / (1:R) McDiarmid's inequality Multidimensional Chebyshev's inequality Paley–Zygmund inequality / (1:R) Pinsker's inequality / (2:R) Vysochanskiï–Petunin inequality / (1:C) |
Markov chain / (FLSU:D) Additive Markov chain Bayesian network / Bay Birth-death process / (U:D) CIR process / scl Chapman–Kolmogorov equation / (F:DC) Cheeger bound / (L:D) Conductance Contact process Continuous-time Markov process / (U:D) Detailed balance / (F:D) Examples of Markov chains / (FL:D) Feller process / (U:G) Fokker–Planck equation / scl anl Foster's theorem / (L:D) Gauss–Markov process / Gau Geometric Brownian motion / scl Hammersley–Clifford theorem / (F:C) Harris chain / (L:DC) Hidden Markov model / (F:D) Hidden Markov random field Hunt process / (U:R) Kalman filter / (F:C) Kolmogorov backward equation / scl Kolmogorov’s criterion / (F:D) Kolmogorov’s generalized criterion / (U:D) |
Krylov–Bogolyubov theorem / anl Lumpability Markov additive process Markov blanket / Bay Markov chain mixing time / (L:D) Markov decision process Markov information source Markov kernel Markov logic network Markov network Markov process / (U:D) Markov property / (F:D) Markov random field Master equation / phs (U:D) Milstein method / scl Moran process Ornstein–Uhlenbeck process / Gau scl Partially observable Markov decision process Product form solution / spr Quantum Markov chain / phs Semi-Markov process Stochastic matrix / anl Telegraph process / (U:B) Variable-order Markov model Wiener process / Gau scl |
Normal distribution / spd Abstract Wiener space Brownian bridge Classical Wiener space Concentration dimension Dudley's theorem / inq Estimation of covariance matrices Fractional Brownian motion Gaussian isoperimetric inequality Gaussian measure / anl Gaussian random field Gauss–Markov process / Mar Integration of the normal density function / spd anl |
Gaussian process Isserlis Gaussian moment theorem / mnt Karhunen–Loève theorem Large deviations of Gaussian random functions / lrd Lévy's modulus of continuity theorem / (U:R) Matrix normal distribution / spd Multivariate normal distribution / spd Ornstein–Uhlenbeck process / Mar scl Paley–Wiener integral / anl Pregaussian class Schilder's theorem / lrd Wiener process / Mar scl |
Conditioning / (2:BDCR) Bayes' theorem / (2:BCG) Borel–Kolmogorov paradox / iex (2:CM) Conditional expectation / (2:BDR) Conditional independence / (3F:BR) Conditional probability Conditional probability distribution / (2:DC) |
Conditional random field / (F:R) Disintegration theorem / anl (2:G) Inverse probability / Bay Luce's choice axiom Regular conditional probability / (2:G) Rule of succession / (F:B) |
Binomial distribution / (1:D) (a,b,0) class of distributions / (1:D) Anscombe transform Bernoulli distribution / (1:B) Beta distribution / (1:C) Bose–Einstein statistics / (F:D) Cantor distribution / (1:C) Cauchy distribution / (1:C) Chi-squared distribution / (1:C) Compound Poisson distribution / (F:DR) Degenerate distribution / (1:D) Dirichlet distribution / (F:C) Discrete phase-type distribution / (1:D) Erlang distribution / (1:C) Exponential-logarithmic distribution / (1:C) Exponential distribution / (1:C) F-distribution / (1:C) Fermi–Dirac statistics / (1F:D) Fisher–Tippett distribution / (1:C) Gamma distribution / (1:C) Generalized normal distribution / (1:C) Geometric distribution / (1:D) Half circle distribution / (1:C) Hypergeometric distribution / (1:D) |
Normal distribution / Gau Integration of the normal density function / Gau anl Lévy distribution / (1:C) Matrix normal distribution / Gau Maxwell–Boltzmann statistics / (F:D) McCullagh's parametrization of the Cauchy distributions / (1:C) Multinomial distribution / (F:D) Multivariate normal distribution / Gau Negative binomial distribution / (1:D) Pareto distribution / (1:C) Phase-type distribution / (1:C) Poisson distribution / (1:D) Power law / (1:C) Skew normal distribution / (1:C) Stable distribution / (1:C) Student's t-distribution / (1:C) Tracy–Widom distribution / rmt Triangular distribution / (1:C) Weibull distribution / (1:C) Wigner semicircle distribution / (1:C) Wishart distribution / (F:C) Zeta distribution / (1:D) Zipf's law / (1:D) |
Donsker's theorem / (LU:C) Empirical distribution function Empirical measure / (FL:RG) (U:D) Empirical process / (FL:RG) (U:D) |
Glivenko–Cantelli theorem / (FL:RG) (U:D) Khmaladze transformation / (FL:RG) (U:D) Vapnik–Chervonenkis theory |
Central limit theorem / (L:R) Berry–Esseen theorem / (F:R) Characteristic function / anl (1F:DCR) De Moivre–Laplace theorem / (L:BD) Helly–Bray theorem / anl (L:R) Illustration of the central limit theorem / (L:DC) Lindeberg's condition |
Lyapunov's central limit theorem / (L:R) Lévy's continuity theorem / anl (L:R) Lévy's convergence theorem / (S:R) Martingale central limit theorem / (S:R) Method of moments / mnt (L:R) Slutsky's theorem / anl Weak convergence of measures / anl |
Large deviations theory Contraction principle Cramér's theorem Exponentially equivalent measures Freidlin–Wentzell theorem Laplace principle |
Large deviations of Gaussian random functions / Gau Rate function Schilder's theorem / Gau Tilted large deviation principle Varadhan's lemma |
Random graph BA model Barabási–Albert model Erdős–Rényi model Percolation theory / phs (L:B) |
Percolation threshold / phs Random geometric graph Random regular graph Watts and Strogatz model |
Random matrix Circular ensemble Gaussian matrix ensemble |
Tracy–Widom distribution / spd Weingarten function / anl |
Itô calculus Bessel process CIR process / Mar Doléans-Dade exponential Dynkin's formula Euler–Maruyama method Feynman–Kac formula Filtering problem Fokker–Planck equation / Mar anl Geometric Brownian motion / Mar Girsanov theorem Green measure Heston model / fnc Hörmander's condition / anl Infinitesimal generator Itô's lemma Itō calculus Itō diffusion Itō isometry Itō's lemma |
Kolmogorov backward equation / Mar Local time Milstein method / Mar Novikov's condition Ornstein–Uhlenbeck process / Gau Mar Quadratic variation Random dynamical system / rds Reversible diffusion Runge–Kutta method Russo–Vallois integral Schramm–Loewner evolution Semimartingale Stochastic calculus Stochastic differential equation Stochastic processes and boundary value problems / anl Stratonovich integral Tanaka equation Tanaka's formula Wiener process / Gau Mar Wiener sausage |
Malliavin calculus Clark–Ocone theorem H-derivative Integral representation theorem for classical Wiener space Integration by parts operator |
Malliavin derivative Malliavin's absolute continuity lemma Ornstein–Uhlenbeck operator Skorokhod integral |
Random dynamical system / scl
Absorbing set
Base flow
Pullback attractor
Probability space Carleman's condition / mnt (1:R) Characteristic function / lmt (1F:DCR) Contiguity#Probability theory Càdlàg Disintegration theorem / cnd (2:G) Dynkin system Exponential family Factorial moment generating function / mnt (1:R) Filtration Fokker–Planck equation / scl Mar Gaussian measure / Gau Hamburger moment problem / mnt (1:R) Hausdorff moment problem / mnt (1:R) Helly–Bray theorem / lmt (L:R) Hörmander's condition / scl Integration of the normal density function / spd Gau Kolmogorov extension theorem / (SU:R) |
Krylov–Bogolyubov theorem / Mar Law (stochastic processes) / (U:G) Location-scale family Lévy's continuity theorem / lmt (L:R) Minlos' theorem Moment problem / mnt (1:R) Moment-generating function / mnt (1F:R) Natural filtration / (U:G) Paley–Wiener integral / Gau Sazonov's theorem Slutsky's theorem / lmt Standard probability space Stieltjes moment problem / mnt (1:R) Stochastic matrix / Mar Stochastic processes and boundary value problems / scl Trigonometric moment problem / mnt (1:R) Weak convergence of measures / lmt Weingarten function / rmt |
Bernoulli trial / (1:B) Complementary event / (1:B) Entropy / (1:BDC) |
Event / (1:B) Indecomposable distribution / (1:BDCR) Indicator function / (1F:B) |
Binomial probability / (1:D) Continuity correction / (1:DC) Entropy / (1:BDC) Equiprobable / (1:D) Hann function / (1:D) Indecomposable distribution / (1:BDCR) Infinite divisibility / (1:DCR) |
Le Cam's theorem / (F:B) (1:D) Limiting density of discrete points / (1:DC) Mean difference / (1:DCR) Memorylessness / (1:DCR) Probability vector / (1:D) Probability-generating function / (1:D) Tsallis entropy / (1:DC) |
Almost surely / (1:C) (LS:D) Continuity correction / (1:DC) Edgeworth series / (1:C) Entropy / (1:BDC) Indecomposable distribution / (1:BDCR) Infinite divisibility / (1:DCR) Limiting density of discrete points / (1:DC) Location parameter / (1:C) |
Mean difference / (1:DCR) Memorylessness / (1:DCR) Monotone likelihood ratio / (1:C) Scale parameter / (1:C) Stability / (1:C) Stein's lemma / (12:C) Truncated distribution / (1:C) Tsallis entropy / (1:DC) |
Heavy-tailed distribution / (1:R) Indecomposable distribution / (1:BDCR) Infinite divisibility / (1:DCR) Locality / (1:R) Mean difference / (1:DCR) |
Memorylessness / (1:DCR) Quantile / (1:R) Survival function / (1:R) Taylor expansions for the moments of functions of random variables / (1:R) |
Bertrand's paradox / (1:M)
Pitman–Yor process / (1:G)
Random compact set / (1:G)
Random element / (1:G)
Coupling / (2:BRG)
Craps principle / (2:B)
Kullback–Leibler divergence / (2:DCR)
Mutual information / (23F:DC)
Copula / (2F:C) Cramér's theorem / (2:C) Kullback–Leibler divergence / (2:DCR) Mutual information / (23F:DC) |
Normally distributed and uncorrelated does not imply independent / (2:C) Posterior probability / Bay (2:C) Stein's lemma / (12:C) |
Coupling / (2:BRG) Hellinger distance / (2:R) Kullback–Leibler divergence / (2:DCR) |
Lévy metric / (2:R) Total variation#Total variation distance in probability theory / (2:R) |
Coupling / (2:BRG)
Lévy–Prokhorov metric / (2:G)
Wasserstein metric / (2:G)
Pairwise independence / (3:B) (F:R)
Mutual information / (23F:DC)
Mutual information / (23F:DC)
Bertrand's ballot theorem / (F:B) Boole's inequality / (FS:B) Coin flipping / (F:B) Collectively exhaustive events / (F:B) Inclusion-exclusion principle / (F:B) Independence / (F:BR) Indicator function / (1F:B) |
Law of total probability / (F:B) Le Cam's theorem / (F:B) (1:D) Leftover hash-lemma / (F:B) Lovász local lemma / (F:B) Mutually exclusive / (F:B) Random walk / (FLS:BD) (U:C) Schuette–Nesbitt formula / (F:B) |
Coupon collector's problem / gmb (F:D) Coupon collector's problem (generating function approach) / gmb (F:D) Graphical model / (F:D) Kirkwood approximation / (F:D) |
Mutual information / (23F:DC) Random field / (F:D) Random walk / (FLS:BD) (U:C) Stopped process / (FU:DG) |
Anderson's theorem#Application to probability theory / (F:C) Autoregressive integrated moving average / (FS:C) Autoregressive model / (FS:C) Autoregressive moving average model / (FS:C) Copula / (2F:C) |
Maxwell's theorem / (F:C) Moving average model / (FS:C) Mutual information / (23F:DC) Schrödinger method / (F:C) |
Bapat–Beg theorem / (F:R) Comonotonicity / (F:R) Doob martingale / (F:R) Independence / (F:BR) Littlewood–Offord problem / (F:R) Lévy flight / (F:R) (U:C) Martingale / (FU:R) Martingale difference sequence / (F:R) |
Maximum likelihood / (FL:R) Multivariate random variable / (F:R) Optional stopping theorem / (FS:R) Pairwise independence / (3:B) (F:R) Stopping time / (FU:R) Time series / (FS:R) Wald's equation / (FS:R) Wick product / (F:R) |
Finite-dimensional distribution / (FU:G)
Hitting time / (FU:G)
Stopped process / (FU:DG)
Random walk / (FLS:BD) (U:C)
Almost surely / (1:C) (LS:D) Gambler's ruin / gmb (L:D) Loop-erased random walk / (L:D) (U:C) |
Preferential attachment / (L:D) Random walk / (FLS:BD) (U:C) Typical set / (L:D) |
Convergence of random variables / (LS:R) Law of large numbers / (LS:R) |
Maximum likelihood / (FL:R) Stochastic convergence / (LS:R) |
Bernoulli process / (S:B) Boole's inequality / (FS:B) Borel–Cantelli lemma / (S:B) |
De Finetti's theorem / (S:B) Exchangeable random variables / (S:BR) Random walk / (FLS:BD) (U:C) |
Almost surely / (1:C) (LS:D) Asymptotic equipartition property / (S:DC) Bernoulli scheme / (S:D) Branching process / (S:D) |
Chinese restaurant process / (S:D) Galton–Watson process / (S:D) Information source / (S:D) Random walk / (FLS:BD) (U:C) |
Asymptotic equipartition property / (S:DC) Autoregressive integrated moving average / (FS:C) Autoregressive model / (FS:C) |
Autoregressive moving average model / (FS:C) Moving average model / (FS:C) |
Big O in probability notation / (S:R) Convergence of random variables / (LS:R) Doob's martingale convergence theorems / (SU:R) Ergodic theory / (S:R) Exchangeable random variables / (S:BR) Hewitt–Savage zero-one law / (S:RG) Kolmogorov's zero-one law / (S:R) Law of large numbers / (LS:R) Law of the iterated logarithm / (S:R) |
Maximal ergodic theorem / (S:R) Op (statistics) / (S:R) Optional stopping theorem / (FS:R) Stationary process / (SU:R) Stochastic convergence / (LS:R) Stochastic process / (SU:RG) Time series / (FS:R) Uniform integrability / (S:R) Wald's equation / (FS:R) |
Hewitt–Savage zero-one law / (S:RG) Mixing / (S:G) |
Skorokhod's representation theorem / (S:G) Stochastic process / (SU:RG) |
Counting process / (U:D) Cox process / (U:D) Dirichlet process / (U:D) Lévy process / (U:DC) Non-homogeneous Poisson process / (U:D) Point process / (U:D) |
Poisson process / (U:D) Poisson random measure / (U:D) Random measure / (U:D) Renewal theory / (U:D) Stopped process / (FU:DG) |
Brownian motion / phs (U:C) Gamma process / (U:C) Loop-erased random walk / (L:D) (U:C) Lévy flight / (F:R) (U:C) |
Lévy process / (U:DC) Martingale representation theorem / (U:C) Random walk / (FLS:BD) (U:C) Skorokhod's embedding theorem / (U:C) |
Compound Poisson process / (U:R) Continuous stochastic process / (U:RG) Doob's martingale convergence theorems / (SU:R) Doob–Meyer decomposition theorem / (U:R) Feller-continuous process / (U:R) Kolmogorov continuity theorem / (U:R) |
Local martingale / (U:R) Martingale / (FU:R) Stationary process / (SU:R) Stochastic process / (SU:RG) Stopping time / (FU:R) |
Adapted process / (U:G) Continuous stochastic process / (U:RG) Finite-dimensional distribution / (FU:G) Hitting time / (FU:G) Killed process / (U:G) |
Progressively measurable process / (U:G) Sample-continuous process / (U:G) Stochastic process / (SU:RG) Stopped process / (FU:DG) |
Aleatoric Average Bean machine Cox's theorem Equipossible Exotic probability Extractor Free probability Frequency Frequency probability Impossible event Infinite monkey theorem Information geometry Law of Truly Large Numbers Littlewood's law |
Observational error Principle of indifference Principle of maximum entropy Probability Probability interpretations Propensity probability Random number generator Random sequence Randomization Randomness Statistical dispersion Statistical regularity Uncertainty Upper and lower probabilities Urn problem |
Algebra of random variables Belief propagation Dempster–Shafer theory Dutch book Elementary event |
Normalizing constant Possibility theory Probability axioms Transferable belief model Unit measure |
Betting Bookmaker Coherence Coupon collector's problem / (F:D) Coupon collector's problem (generating function approach) / (F:D) Gambler's fallacy Gambler's ruin / (L:D) Game of chance Inverse gambler's fallacy Lottery Lottery machine Luck Martingale |
Odds Pachinko Parimutuel betting Parrondo's paradox Pascal's wager Poker probability Poker probability (Omaha) Poker probability (Texas hold 'em) Pot odds Proebsting's paradox Roulette Spread betting The man who broke the bank at Monte Carlo |
Bible code Birthday paradox Birthday problem |
Index of coincidence Spurious relationship |
Algorithmic Lovász local lemma Box–Muller transform Gibbs sampling Inverse transform sampling method Las Vegas algorithm Metropolis algorithm Monte Carlo method |
Panjer recursion Probabilistic Turing machine Probabilistic algorithm Probabilistically checkable proof Probable prime Stochastic programming |
Bayes factor Bayesian model comparison Bayesian network / Mar Bayesian probability Bayesianism Checking if a coin is fair Conjugate prior Factor graph Good–Turing frequency estimation |
Imprecise probability Inverse probability / cnd Marginal likelihood Markov blanket / Mar Posterior probability / (2:C) Prior probability SIPTA Subjective logic Subjectivism#Subjectivism in probability / hst |
Allais paradox Black–Scholes Cox–Ingersoll–Ross model Forward measure Heston model / scl Jump process Jump-diffusion model Kelly criterion Market risk Mathematics of bookmaking |
Risk Risk-neutral measure Ruin theory Sethi model Technical analysis Value at risk Variance gamma process / spr Vasicek model Volatility |
Boltzmann factor Brownian motion / (U:C) Brownian ratchet Cosmic variance Critical phenomena Diffusion-limited aggregation Fluctuation theorem Gibbs state Information entropy Lattice model Master equation / Mar (U:D) Negative probability |
Nonextensive entropy Partition function Percolation theory / rgr (L:B) Percolation threshold / rgr Probability amplitude Quantum Markov chain / Mar Quantum probability Scaling limit Statistical mechanics Statistical physics Vacuum expectation value |
Ewens's sampling formula Hardy–Weinberg principle Population genetics |
Punnett square Ronald Fisher |
Anomaly time series Arrival theorem Beverton–Holt model Burke's theorem Buzen's algorithm Disorder problem Erlang unit G-network Gordon–Newell theorem Innovation Jump diffusion M/M/1 model M/M/c model |
Mark V Shaney Markov chain Monte Carlo Markov switching multifractal Oscillator linewidth Poisson hidden Markov model Population process Product form solution / Mar Quasireversibility Queueing theory Recurrence period density entropy Variance gamma process / fnc Wiener equation |
Boolean model Buffon's needle Geometric probability Hadwiger's theorem |
Integral geometry Random coil Stochastic geometry Vitale's random Brunn–Minkowski inequality |
Benford's law
Pareto principle
History of probability Newton–Pepys problem Problem of points Subjectivism#Subjectivism in probability / Bay |
Sunrise problem The Doctrine of Chances |
B-convex space Conditional event algebra Error function Goodman–Nguyen–van Fraassen algebra List of mathematical probabilists |
Nuisance variable Probabilistic encryption Probabilistic logic Probabilistic proofs of non-probabilistic theorems Pseudocount |
"Core": 455 (570) "Around": 198 (200) |
"Core selected": 311 (358) "Core others": 144 (212) |
Here k(n) means: n links to k articles. (Some articles are linked more than once.)