List of probability topics

This is a list of probability topics, by Wikipedia page. It overlaps with the (alphabetical) list of statistical topics. There are also the list of probabilists and list of statisticians.

General aspects

*Probability
*Randomness, Pseudorandomness, Quasirandom
*Randomization, hardware random number generator
*Random number generator
*Random sequence
*Coin flipping/tossing; checking if a coin is biased
*Uncertainty
*Statistical dispersion
*Observational error
*Average
*Probability interpretations
*Markovian
*Statistical regularity
*Central tendency
*Bean machine
*Relative frequency
*Frequency probability
*Maximum likelihood
*Bayesian probability
*Principle of indifference
*Cox's theorem
*Principle of maximum entropy
*Information entropy
*Urn problems
*Extractor
*Aleatoric, aleatoric music
*Free probability
*Exotic probability
*Schrödinger method
*Kolmogorov's zero-one law
*Hewitt-Savage zero-one law

Foundations of probability theory

*Probability theory
*Sample space
*Probability space
*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
*Edwin Thompson Jaynes
*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
**Probability mass function
*Constant random variable
*Expected value
**Jensen's inequality
*Variance
**Standard deviation
**Geometric standard deviation
*Moment (mathematics)
**Moment about the mean
**Standardized moment
***Skewness
***Kurtosis
***Locality
**Cumulant
**Factorial moment
**Moment problem
*Multivariate random variable
*Independent 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
*Markov's inequality
*Chebyshev's inequality
*Chernoff's inequality
*Laws of large numbers
**Asymptotic equipartition property
**Typical set
*Random field
*Borel-Cantelli lemma
*Wick product

Conditional probability

*Conditional expectation
*Conditional distribution
*Marginal distribution
*Bayes' theorem
*de Finetti's theorem
*Rule of succession
*Conditional independence

Probability distributions

*Bose-Einstein statistics
*Bernoulli distribution
**Bernoulli trial
*Beta distribution
*Binomial distribution
*Cantor distribution
*Cauchy distribution
**McCullagh's parametrization of the Cauchy distributions
*Chi-square distribution
*Continuity correction
*Copula (statistics)
*Coupon collector's problem
*Degenerate distribution
*Dirichlet distribution
*Erlang distribution
*Exponential distribution
**Exponential family
*F-distribution
*Fermi-Dirac statistics
*Fisher-Tippett distribution
*Gamma distribution
*Geometric distribution
*Graphical model
*Hypergeometric distribution
*Lévy distribution
*Levy skew alpha-stable distribution
*Maxwell-Boltzmann statistics
*Moment (mathematics)
**Moment about the mean
**Standardized moment
***Skewness
***Kurtosis
***Locality
**Cumulant
**Factorial moment
**Expected value
**Variance
**An inequality on location and scale parameters
**Taylor expansions for the moments of functions of random variables
*Multinomial distribution
*Negative binomial distribution
*Negative hypergeometric distribution
*Normal distribution, also called the Gaussian distribution
**Error function
**Multivariate normal distribution
**Matrix normal distribution
*Memorylessness
*Pareto distribution
*Phase-type distribution
*Poisson distribution
**Compound Poisson distribution
*Prior probability distribution
*stable distributions
*Student's t-distribution
*Total variation distance
*Triangular distribution
*Weibull distribution
*Wigner semicircle distribution
*Wishart distribution
*Zeta distribution
*Infinitely divisible distribution
*Indecomposable distribution

Properties of probability distributions

*Central limit theorem
**Illustration of the central limit theorem
**Concrete illustration of the central limit theorem
**Berry-Esséen theorem
*Martingale central limit theorem
*Characteristic function (probability theory)
*Edgeworth series
*Helly-Bray theorem
*Limit 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
*Stability (probability)

Applied probability

*"Empirical findings"
**Benford's law
**Pareto principle
**Zipf's law

Stochastic processes

*Adapted process
*Bernoulli process
**Bernoulli scheme
*Branching process
*Brownian motion
**Geometric Brownian motion
**Wiener equation
*Chapman-Kolmogorov equation
*Chinese restaurant process
*Coupling (probability)
*Ergodic theory
*Galton–Watson process
*Gauss-Markov process
*Gaussian process
*Girsanov's theorem
*Itô's lemma
*Law of the iterated logarithm
*Lévy flight
*Lévy process
*Loop-erased random walk
*Markov chain
**Continuous-time Markov process
**Examples of Markov chains
*Markov property
**Hidden Markov model
*Martingale
**Martingale representation theorem
**Azuma's inequality
**Wald's equation
*Poisson process
*Population process
*Process with independent increments
*Progressively measurable process
*Queueing theory
**Erlang unit
*Random walk
*Random walk Monte Carlo
*Skorokhod's embedding theorem
*Stationary process
*Stochastic calculus
**Itô calculus
**Malliavin calculus
**Stratonovich integral
*Time series analysis
**Autoregressive moving average model
**Autoregressive integrated moving average model
**Anomaly time series
*Wiener process

Geometric probability

*Buffon's needle
*Integral geometry
*Hadwiger's theorem

Statistics

*List of statistical topics
*Statistical sample
**Sampling (statistics)
**Data point
**Data set
**Statistical population
*Statistical theory
*Statistical inference
*Null hypothesis
*Confidence interval
*Margin of error
*Interval estimation
*point estimation
*Estimator
*Bias (statistics)
*Gauss-Markov theorem
*Likelihood-ratio test
*Multivariate statistics
*Analysis of variance
*ANCOVA
*Bayesian inference

Applied statistics

*Linear regression
*Instrumental variable
*Statistical unit
*Statistical assembly
*Statistical model

Gambling

*Luck, chance
*Game of chance
*Odds
*Betting
**Spread betting
*Bookmaker
*Parimutuel betting
*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)
**The man who broke the bank at Monte Carlo
*Lottery
**Lottery machine
**Pachinko
*Coherence (philosophical gambling strategy)
*Coupon collector's problem

Coincidence

*Birthday paradox
*Index of coincidence
*Bible code
*Spurious relationship

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

Financial mathematics

*Risk
*Value at risk
*Market risk
*Risk-neutral measure
*Volatility
*Technical analysis

Physics

*Probability amplitude
*Statistical physics
*Boltzmann factor
*Feynman-Kac formula
*Fluctuation theorem
*Information entropy
*Vacuum expectation value
*Brownian ratchet
*Cosmic variance
*Negative probability

Percolation theory

Genetics

*Punnett square
*Hardy-Weinberg principle
*Ewens's sampling formula
*Ronald Fisher
*Population genetics

Historical

*"The Doctrine of Chances"