Catalog of articles in probability theory
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, which refers to number of random variables involved and the type of the distribution. For example 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.
Core probability: selected topics
'''Probability theory'''Basic notions (bsc)
Random variable- Continuous probability distribution /
- Cumulative distribution function /
- Discrete probability distribution /
- Independent and identically-distributed random variables /
- Joint probability distribution /
- Marginal distribution /
- Probability density function /
- Probability distribution /
- Probability distribution function
- Probability mass function /
- Sample space
Instructive examples (paradoxes) (iex)
- Berkson's paradox /
- Bertrand's box paradox /
- Borel–Kolmogorov paradox / cnd
- Boy or Girl paradox /
- Exchange paradox /
- Intransitive dice
- Monty Hall problem /
- Necktie paradox
- Simpson's paradox
- Sleeping Beauty problem
- St. Petersburg paradox / mnt
- Three Prisoners problem
- Two envelopes problem
Moments (mnt)
Expected value /- Canonical correlation /
- Carleman's condition / anl
- Central moment /
- Coefficient of variation /
- Correlation /
- Correlation function /
- Covariance /
- Covariance function /
- Covariance matrix /
- Cumulant /
- Factorial moment /
- Factorial moment generating function / anl
- Fano factor
- Geometric standard deviation /
- Hamburger moment problem / anl
- Hausdorff moment problem / anl
- Isserlis Gaussian moment theorem / Gau
- Jensen's inequality /
- Kurtosis /
- Law of the unconscious statistician / Moment /
- Law of total covariance /
- Law of total cumulance /
- Law of total expectation /
- Law of total variance /
- Logmoment generating function
- Marcinkiewicz–Zygmund inequality / inq
- Method of moments / lmt
- Moment problem / anl
- Moment-generating function / anl
- Second moment method /
- Skewness /
- St. Petersburg paradox / iex
- Standard deviation /
- Standardized moment /
- Stieltjes moment problem / anl
- Trigonometric moment problem / anl
- Uncorrelated /
- Variance /
- Variance-to-mean ratio /
Inequalities (inq)
Chebyshev's inequality /- An inequality on location and scale parameters /
- Azuma's inequality /
- Bennett's inequality /
- Bernstein inequalities /
- Bhatia–Davis inequality
- Chernoff bound /
- Doob's martingale inequality /
- Dudley's theorem / Gau
- Entropy power inequality
- Etemadi's inequality /
- Gauss's inequality
- Hoeffding's inequality /
- Khintchine inequality /
- Kolmogorov's inequality /
- Marcinkiewicz–Zygmund inequality / mnt
- Markov's inequality /
- McDiarmid's inequality
- Multidimensional Chebyshev's inequality
- Paley–Zygmund inequality /
- Pinsker's inequality /
- Vysochanskiï–Petunin inequality /
Markov chains, processes, fields, networks (Mar)
Markov chain /- Additive Markov chain
- Bayesian network / Bay
- Birth–death process /
- CIR process / scl
- Chapman–Kolmogorov equation /
- Cheeger bound /
- Conductance
- Contact process
- Continuous-time Markov process /
- Detailed balance /
- Examples of Markov chains /
- Feller process /
- Fokker–Planck equation / scl anl
- Foster's theorem /
- Gauss–Markov process / Gau
- Geometric Brownian motion / scl
- Hammersley–Clifford theorem /
- Harris chain /
- Hidden Markov model /
- Hidden Markov random field
- Hunt process /
- Kalman filter /
- Kolmogorov backward equation / scl
- Kolmogorov's criterion /
- Kolmogorov's generalized criterion /
- Krylov–Bogolyubov theorem / anl
- Lumpability
- Markov additive process
- Markov blanket / Bay
- Markov chain mixing time /
- Markov decision process
- Markov information source
- Markov kernel
- Markov logic network
- Markov network
- Markov process /
- Markov property /
- Markov random field
- Master equation / phs
- 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 /
- Variable-order Markov model
- Wiener process / Gau scl
Gaussian random variables, vectors, functions (Gau)
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 anlGaussian process
- Isserlis Gaussian moment theorem / mnt
- Karhunen–Loève theorem
- Large deviations of Gaussian random functions / lrd
- Lévy's modulus of continuity theorem /
- 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 (cnd)
Conditioning /- Bayes' theorem /
- Borel–Kolmogorov paradox / iex
- Conditional expectation /
- Conditional independence /
- Conditional probability
- Conditional probability distribution /
- Conditional random field /
- Disintegration theorem / anl
- Inverse probability / Bay
- Luce's choice axiom
- Regular conditional probability /
- Rule of succession /
Specific distributions (spd)
Binomial distribution /- (a,b,0) class of distributions /
- Anscombe transform
- Bernoulli distribution /
- Beta distribution /
- Bose-Einstein statistics /
- Cantor distribution /
- Cauchy distribution /
- Chi-squared distribution /
- Compound Poisson distribution /
- Degenerate distribution /
- Dirichlet distribution /
- Discrete phase-type distribution /
- Erlang distribution /
- Exponential-logarithmic distribution /
- Exponential distribution /
- F-distribution /
- Fermi-Dirac statistics /
- Fisher-Tippett distribution /
- Gamma distribution /
- Generalized normal distribution /
- Geometric distribution /
- Half circle distribution /
- Hypergeometric distribution / Normal distribution / Gau
- Integration of the normal density function / Gau anl
- Lévy distribution /
- Matrix normal distribution / Gau
- Maxwell-Boltzmann statistics /
- McCullagh's parametrization of the Cauchy distributions /
- Multinomial distribution /
- Multivariate normal distribution / Gau
- Negative binomial distribution /
- Pareto distribution /
- Phase-type distribution /
- Poisson distribution /
- Power law /
- Skew normal distribution /
- Stable distribution /
- Student's t-distribution /
- Tracy–Widom distribution / rmt
- Triangular distribution /
- Weibull distribution /
- Wigner semicircle distribution /
- Wishart distribution /
- Zeta distribution /
- Zipf's law /
Empirical measure (emm)
- Donsker's theorem /
- Empirical distribution function
- Empirical measure /
- Empirical process /
- Glivenko–Cantelli theorem /
- Khmaladze transformation /
- Vapnik–Chervonenkis theory
Limit theorems (lmt)
Central limit theorem /- Berry–Esseen theorem /
- Characteristic function / anl
- De Moivre–Laplace theorem /
- Helly–Bray theorem / anl
- Illustration of the central limit theorem /
- Lindeberg's condition
- Lyapunov's central limit theorem /
- Lévy's continuity theorem / anl
- Lévy's convergence theorem /
- Martingale central limit theorem /
- Method of moments / mnt
- Slutsky's theorem / anl
- Weak convergence of measures / anl
Large deviations (lrd)
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 graphs (rgr)
Random graph- BA model
- Barabási–Albert model
- Erdős–Rényi model
- Percolation theory / phs
- Percolation threshold / phs
- Random geometric graph
- Random regular graph
- Watts and Strogatz model
Random matrices (rmt)
Random matrixStochastic calculus (scl)
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
- Itô calculus
- Itô diffusion
- Itô isometry
- Itô'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 (Mal)
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 systems (rds)
Random dynamical system / sclAnalytic aspects (including measure theoretic) (anl)
Probability space- Carleman's condition / mnt
- Characteristic function / lmt
- Contiguity#Probability theory
- Càdlàg
- Disintegration theorem / cnd
- Dynkin system
- Exponential family
- Factorial moment generating function / mnt
- Filtration
- Fokker–Planck equation / scl Mar
- Gaussian measure / Gau
- Hamburger moment problem / mnt
- Hausdorff moment problem / mnt
- Helly–Bray theorem / lmt
- Hörmander's condition / scl
- Integration of the normal density function / spd Gau
- Kolmogorov extension theorem /
- Krylov–Bogolyubov theorem / Mar
- Law (stochastic processes) /
- Location-scale family
- Lévy's continuity theorem / lmt
- Minlos' theorem
- Moment problem / mnt
- Moment-generating function / mnt
- Natural filtration /
- Paley–Wiener integral / Gau
- Sazonov's theorem
- Slutsky's theorem / lmt
- Standard probability space
- Stieltjes moment problem / mnt
- Stochastic matrix / Mar
- Stochastic processes and boundary value problems / scl
- Trigonometric moment problem / mnt
- Weak convergence of measures / lmt
- Weingarten function / rmt
Core probability: other articles, by number and type of random variables
A single random variable (1:)
Binary (1:B)
- Bernoulli trial /
- Complementary event /
- Entropy /
- Event /
- Indecomposable distribution /
- Indicator function /
Discrete (1:D)
- Binomial probability /
- Continuity correction /
- Entropy /
- Equiprobable /
- Hann function /
- Indecomposable distribution /
- Infinite divisibility /
- Le Cam's theorem /
- Limiting density of discrete points /
- Mean difference /
- Memorylessness /
- Probability vector /
- Probability-generating function /
- Tsallis entropy /
Continuous (1:C)
- Almost surely /
- Continuity correction /
- Edgeworth series /
- Entropy /
- Indecomposable distribution /
- Infinite divisibility /
- Limiting density of discrete points /
- Location parameter /
- Mean difference /
- Memorylessness /
- Monotone likelihood ratio /
- Scale parameter /
- Stability /
- Stein's lemma /
- Truncated distribution /
- Tsallis entropy /
Real-valued, arbitrary (1:R)
- Heavy-tailed distribution /
- Indecomposable distribution /
- Infinite divisibility /
- Locality /
- Mean difference /
- Memorylessness /
- Quantile /
- Survival function /
- Taylor expansions for the moments of functions of random variables /
Random point of a manifold (1:M)
General (random element of an abstract space) (1:G)
Two random variables (2:)
Binary (2:B)
Discrete (2:D)
Continuous (2:C)
- Copula /
- Cramér's theorem /
- Kullback–Leibler divergence /
- Mutual information /
- Normally distributed and uncorrelated does not imply independent /
- Posterior probability / Bay
- Stein's lemma /
Real-valued, arbitrary (2:R)
- Coupling /
- Hellinger distance /
- Kullback–Leibler divergence /
- Lévy metric /
- Total variation#Total variation distance in probability theory /
General (random element of an abstract space) (2:G)
Three random variables (3:)
Binary (3:B)
Discrete (3:D)
Continuous (3:C)
Finitely many random variables (F:)
Binary (F:B)
- Bertrand's ballot theorem /
- Boole's inequality /
- Coin flipping /
- Collectively exhaustive events /
- Inclusion–exclusion principle /
- Independence /
- Indicator function /
- Law of total probability /
- Le Cam's theorem /
- Leftover hash lemma /
- Lovász local lemma /
- Mutually exclusive /
- Random walk /
- Schuette–Nesbitt formula /
Discrete (F:D)
- Coupon collector's problem / gmb
- Graphical model /
- Kirkwood approximation /
- Mutual information /
- Random field /
- Random walk /
- Stopped process /
Continuous (F:C)
- Anderson's theorem#Application to probability theory /
- Autoregressive integrated moving average /
- Autoregressive model /
- Autoregressive moving average model /
- Copula /
- Maxwell's theorem /
- Moving average model /
- Mutual information /
- Schrödinger method /
Real-valued, arbitrary (F:R)
- Bapat–Beg theorem /
- Comonotonicity /
- Doob martingale /
- Independence /
- Littlewood–Offord problem /
- Lévy flight /
- Martingale /
- Martingale difference sequence /
- Maximum likelihood /
- Multivariate random variable /
- Optional stopping theorem /
- Pairwise independence /
- Stopping time /
- Time series /
- Wald's equation /
- Wick product /
General (random element of an abstract space) (F:G)
A large number of random variables (finite but tending to infinity) (L:)
Binary (L:B)
Discrete (L:D)
- Almost surely /
- Gambler's ruin / gmb
- Loop-erased random walk /
- Preferential attachment /
- Random walk /
- Typical set /
Real-valued, arbitrary (L:R)
- Convergence of random variables /
- Law of large numbers /
- Maximum likelihood /
- Stochastic convergence /
An infinite sequence of random variables (S:)
Binary (S:B)
- Bernoulli process /
- Boole's inequality /
- Borel–Cantelli lemma /
- De Finetti's theorem /
- Exchangeable random variables /
- Random walk /
Discrete (S:D)
- Almost surely /
- Asymptotic equipartition property /
- Bernoulli scheme /
- Branching process /
- Chinese restaurant process /
- Galton–Watson process /
- Information source /
- Random walk /
Continuous (S:C)
- Asymptotic equipartition property /
- Autoregressive integrated moving average /
- Autoregressive model /
- Autoregressive–moving-average model /
- Moving-average model /
Real-valued, arbitrary (S:R)
- Big O in probability notation /
- Convergence of random variables /
- Doob's martingale convergence theorems /
- Ergodic theory /
- Exchangeable random variables /
- Hewitt–Savage zero–one law /
- Kolmogorov's zero–one law /
- Law of large numbers /
- Law of the iterated logarithm /
- Maximal ergodic theorem /
- Op (statistics) /
- Optional stopping theorem /
- Stationary process /
- Stochastic convergence /
- Stochastic process /
- Time series /
- Uniform integrability /
- Wald's equation /
General (random element of an abstract space) (S:G)
Uncountably many random variables (continuous-time processes etc) (U:)
Discrete (U:D)
- Counting process /
- Cox process /
- Dirichlet process /
- Lévy process /
- Non-homogeneous Poisson process /
- Point process /
- Poisson process /
- Poisson random measure /
- Random measure /
- Renewal theory /
- Stopped process /
Continuous (U:C)
- Brownian motion / phs
- Gamma process /
- Loop-erased random walk /
- Lévy flight /
- Lévy process /
- Martingale representation theorem /
- Random walk /
- Skorokhod's embedding theorem /
Real-valued, arbitrary (U:R)
- Compound Poisson process /
- Continuous stochastic process /
- Doob's martingale convergence theorems /
- Doob–Meyer decomposition theorem /
- Feller-continuous process /
- Kolmogorov continuity theorem /
- Local martingale /
- Martingale /
- Stationary process /
- Stochastic process /
- Stopping time /
General (random element of an abstract space) (U:G)
- Adapted process /
- Continuous stochastic process /
- Finite-dimensional distribution /
- Hitting time /
- Killed process /
- Progressively measurable process /
- Sample-continuous process /
- Stochastic process /
- Stopped process /
Around the core
General aspects (grl)
- 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
Foundations of probability theory (fnd)
- Algebra of random variables
- Belief propagation
- Dempster–Shafer theory
- Dutch book
- Elementary event
- Normalizing constant
- Possibility theory
- Probability axioms
- Transferable belief model
- Unit measure
Gambling (gmb)
- Betting
- Bookmaker
- Coherence
- Coupon collector's problem /
- Coupon collector's problem (generating function approach) /
- Gambler's fallacy
- Gambler's ruin /
- 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
Coincidence (cnc)
Algorithmics (alg)
- 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
Bayesian approach (Bay)
- Bayes factor
- Bayesian model comparison
- Bayesian network / Mar
- Bayesian probability
- Bayesian programming
- 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 /
- Prior probability
- SIPTA
- Subjective logic
- Subjectivism#Subjectivism in probability / hst
Financial mathematics (fnc)
- 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
Physics (phs)
- Boltzmann factor
- Brownian motion /
- Brownian ratchet
- Cosmic variance
- Critical phenomena
- Diffusion-limited aggregation
- Fluctuation theorem
- Gibbs state
- Information entropy
- Lattice model
- Master equation / Mar
- Negative probability
- Nonextensive entropy
- Partition function
- Percolation theory / rgr
- Percolation threshold / rgr
- Probability amplitude
- Quantum Markov chain / Mar
- Quantum probability
- Scaling limit
- Statistical mechanics
- Statistical physics
- Vacuum expectation value
Genetics (gnt)
Stochastic process (spr)
- Anomaly time series
- Arrival theorem
- Beverton–Holt model
- Burke's theorem
- Buzen's algorithm
- Disorder problem
- Erlang unit
- G-network
- Gordon–Newell theorem
- Innovation
- Interacting particle system
- 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
- Probabilistic cellular automata
- Product-form solution / Mar
- Quasireversibility
- Queueing theory
- Recurrence period density entropy
- Variance gamma process / fnc
- Wiener equation
Geometric probability (geo)
- Boolean model
- Buffon's needle
- Geometric probability
- Hadwiger's theorem
- Integral geometry
- Random coil
- Stochastic geometry
- Vitale's random Brunn–Minkowski inequality
Empirical findings (emp)
Historical (hst)
- History of probability
- Newton–Pepys problem
- Problem of points
- Subjectivism#Subjectivism in probability / Bay
- Sunrise problem
- The Doctrine of Chances
Miscellany (msc)
- 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
Counters of articles
- "Core": 455
- "Around": 198
- "Core selected": 311
- "Core others": 144