List of probability topics
408108
218375063
2008-06-10T10:54:21Z
193.74.217.162
/* Stochastic processes */
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 problem]]s
*[[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 (probability)|Bertrand's paradox]]
*[[Coherence (philosophical gambling strategy)]]
*[[Dutch book]]
*[[Algebra of random variables]]
*[[Belief propagation]]
*[[Transferable belief model]]
*[[Dempster-Shafer 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]]
*[[Moment (mathematics)]]
**[[Moment about the mean]]
**[[Standardized moment]]
***[[Skewness]]
***[[Kurtosis]]
***[[Locality (statistics)|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 distribution]]s==
*[[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 (statistics)|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]]
*[[Stability (probability)|stable distributions]]
*[[Student's t-distribution]]
*[[Total variation|Total variation distance]]
*[[Triangular distribution]]
*[[Weibull distribution]]
*[[Wigner semicircle distribution]]
*[[Wishart distribution]]
*[[Zeta distribution]]
*[[Infinite divisibility|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-Esseen 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]]
*[[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 process]]es==
*[[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 (probability theory)|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 phenomena]]
*[[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]]
==[[Percolation theory]]==
==[[Genetics]]==
*[[Punnett square]]
*[[Hardy-Weinberg principle]]
*[[Ewens's sampling formula]]
*[[Ronald Fisher]]
*[[Population genetics]]
==Historical==
*''[[The Doctrine of Chances]]''
[[Category:Mathematics-related lists|Probability]]
[[Category:Probability and statistics| ]]
[[Category:Topical indexes|Probability topics]]