# 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 (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.

## Core probability: selected topics

Probability theory

### Basic notions (bsc)

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

Boy or Girl paradox / (2:B)
Monty Hall problem / (F:B)
Nontransitive dice
Sleeping Beauty problem
St. Petersburg paradox / mnt (1:D)
Three Prisoners problem
Two envelopes problem

### Moments (mnt)

Expected value / (12:DCR)
Canonical correlation / (F:R)
Carleman's condition / anl (1:R)
Central moment / (1:R)
Coefficient of variation / (1:R)
Correlation / (2:R)
Correlation function / (U:R)
Covariance / (2F:R) (1:G)
Covariance function / (U:R)
Covariance matrix / (F:R)
Cumulant / (12F:DCR)
Factorial moment / (1:R)
Factorial moment generating function / anl (1:R)
Fano factor
Geometric standard deviation / (1:R)
Hamburger moment problem / anl (1:R)
Hausdorff moment problem / anl (1:R)
Isserlis Gaussian moment theorem / Gau
Jensen's inequality / (1:DCR)
Kurtosis / (1:CR)
Law of the unconscious statistician / (1:DCR)
Moment / (12FU:CRG)
Law of total covariance / (F:R)
Law of total cumulance / (F:R)
Law of total expectation / (F:DR)
Law of total variance / (F:R)
Logmoment generating function
Marcinkiewicz–Zygmund inequality / inq
Method of moments / lmt (L:R)
Moment problem / anl (1:R)
Moment-generating function / anl (1F:R)
Second moment method / (1FL:DR)
Skewness / (1:R)
St. Petersburg paradox / iex (1:D)
Standard deviation / (1:DCR)
Standardized moment / (1:R)
Stieltjes moment problem / anl (1:R)
Trigonometric moment problem / anl (1:R)
Uncorrelated / (2:R)
Variance / (12F:DCR)
Variance-to-mean ratio / (1:R)

### Inequalities (inq)

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
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 chains, processes, fields, networks (Mar)

Markov chain / (FLSU:D)
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 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

### Conditioning (cnd)

Conditioning / (2:BDCR)
Bayes' theorem / (2:BCG)
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)

### Specific distributions (spd)

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)

### Empirical measure (emm)

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)
Vapnik–Chervonenkis theory

### Limit theorems (lmt)

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

### Analytic aspects (including measure theoretic) (anl)

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

## Core probability: other articles, by number and type of random variables

### A single random variable (1:)

#### Binary (1:B)

Bernoulli trial / (1:B)
Complementary event / (1:B)
Entropy / (1:BDC)
Event / (1:B)
Indecomposable distribution / (1:BDCR)
Indicator function / (1F:B)

#### Discrete (1:D)

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)

#### Continuous (1:C)

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)

#### Real-valued, arbitrary (1:R)

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)

#### General (random element of an abstract space) (1:G)

Pitman–Yor process / (1:G)
Random compact set / (1:G)
Random element / (1:G)

### Two random variables (2:)

#### Binary (2:B)

Coupling / (2:BRG)
Craps principle / (2:B)

#### Discrete (2:D)

Kullback–Leibler divergence / (2:DCR)
Mutual information / (23F:DC)

#### Continuous (2:C)

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)

#### Real-valued, arbitrary (2:R)

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)

#### General (random element of an abstract space) (2:G)

Coupling / (2:BRG)
Lévy–Prokhorov metric / (2:G)
Wasserstein metric / (2:G)

### Three random variables (3:)

#### Binary (3:B)

Pairwise independence / (3:B) (F:R)

#### Discrete (3:D)

Mutual information / (23F:DC)

#### Continuous (3:C)

Mutual information / (23F:DC)

### Finitely many random variables (F:)

#### Binary (F:B)

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)

#### Discrete (F:D)

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)

#### Continuous (F:C)

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)

#### Real-valued, arbitrary (F:R)

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)

#### General (random element of an abstract space) (F:G)

Finite-dimensional distribution / (FU:G)
Hitting time / (FU:G)
Stopped process / (FU:DG)

### A large number of random variables (finite but tending to infinity) (L:)

#### Binary (L:B)

Random walk / (FLS:BD) (U:C)

#### Discrete (L:D)

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)

#### Real-valued, arbitrary (L:R)

Convergence of random variables / (LS:R)
Law of large numbers / (LS:R)
Maximum likelihood / (FL:R)
Stochastic convergence / (LS:R)

### An infinite sequence of random variables (S:)

#### Binary (S:B)

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)

#### Discrete (S:D)

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)

#### Continuous (S: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)

#### Real-valued, arbitrary (S:R)

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)

#### General (random element of an abstract space) (S:G)

Hewitt–Savage zero-one law / (S:RG)
Mixing / (S:G)
Skorokhod's representation theorem / (S:G)
Stochastic process / (SU:RG)

### Uncountably many random variables (continuous-time processes etc) (U:)

#### Discrete (U:D)

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)

#### Continuous (U:C)

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)

#### Real-valued, arbitrary (U:R)

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)

#### General (random element of an abstract space) (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)

## Counters of articles

"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.)