This page gathers the 49 dictionary entries belonging to the domain “Probability theory”, as labelled by Wiktionary. Each word leads to its full entry: definitions, etymology, pronunciation, examples.
- almost adv Up to a null set; except for a set of measure 0.
- binary distribution noun Bernoulli distribution.
- binomial distribution noun The discrete probability distribution of the number of successes in a sequence of n independent trials, each of which yields success with…
- birthday paradox noun The counterintuitive observation that a random group of people needs to have only 23 members before there is a 50% chance of two of them…
- birthday problem noun The mathematics problem that concerns the probability there exist two people in a random group who share a birthday.
- Boole's inequality noun The statement that the probability that at least one of a finite or countable set of events happens is no greater than the sum of the…
- branching process noun A stochastic process which typically models reproduction of objects, with the assumption that the reproductions of individual particles are…
- certain event noun An event that contains all of the possible outcomes and thus is known a priori to be certain to occur;
- characteristic function noun A complex function completely defining the probability distribution of a real-valued random variable
- Chinese restaurant process noun A discrete-time stochastic process, analogous to seating customers at tables in a restaurant, such that, at time n, the n customers have…
- comonotonic adj Of a random vector, having components that can be represented as increasing functions of a single random variable.
- conditional probability distribution noun The probability distribution of a random variable given the known outcome of another random variable.
- detailed balance noun a Markov process is said to show detailed balance if the transition rates between each pair of states i and j in the state space obey
- discrete-time Markov chain noun A sequence of random variables, known as a stochastic process, in which the value of the next variable depends only on the value of the…
- error function noun A sigmoid function giving the probability that a measurement, under the influence of normally distributed errors with standard deviation…
- event noun A set of some of the possible outcomes; a subset of the sample space.
- fair coin noun A sequence of independent Bernoulli trials (a Bernoulli process) with probability 1/2 of success on each trial.
- filtration noun A totally ordered collection of subsets.
- gamma distribution noun Any of a family of two-parameter continuous probability distributions, of which the common exponential distribution and chi-square…
- Gumbel distribution noun A model of the distribution of the maximum (or the minimum) of a number of samples of various distributions.
- homogeneous adj Informally: Determined by its restriction to the unit sphere. Formally: Such that, for all real t>0 and test functions ϕ( mathbf x), the…
- hypergeometric distribution noun A discrete probability distribution that describes the probability of k "successes" in a sequence of n draws without replacement from a…
- Kelly criterion noun A formula used to determine the optimal size of a series of bets in order to maximize the logarithm of wealth.
- likelihood noun The probability that some fixed outcome was generated by a random distribution with a specific parameter.
- Little's law noun A theorem which states that the long-term average number L of customers in a stationary system is equal to the long-term average effective…
- Markov process noun Any stochastic process for which the conditional probability distribution of future states depends only on the current state (and not on…
- Markov property noun The memoryless property of Markov models, according to which the future states depend only on the current state and not those that preceded…
- mean hitting time noun The average number of steps that a Markov chain takes to go from a specified starting state to a specified target state or set of states.
- memoryless adj Of a probability distribution, such that any derived probability from a set of random samples is distinct and has no information (i.e.…
- memorylessness noun The property of being memoryless.
- multi-armed bandit noun An algorithm that allocates a fixed limited set of resources between competing alternative choices so as to maximize the expected gain…
- multichain noun A multichain Markov chain.
- mutually exclusive adj Describing multiple events or propositions such that the occurrence of any one implies the nonoccurrence of all other events or…
- normal adj Which has a very specific bell curve shape; that is or has the qualities of a normal distribution.
- outcome noun The result of a random trial. An element of a sample space.
- probabilistic adj Of, pertaining to, or derived using probability.
- probability density function noun Any function whose integral over a set gives the probability that a random variable has a value in that set.
- quasireversibility noun A property of some queues, differing from reversibility in that a stronger condition is imposed on arrival rates and a weaker condition is…
- Rademacher distribution noun A discrete probability distribution where a random variate has a 50% chance of being +1 and a 50% chance of being -1.
- sample point noun A point in the sample space representing some concrete non-decomposable result of an individual experiment.
- secretary problem noun The problem of selecting the best out of n applicants for a position, under the condition that all applicants are interviewed in random…
- semi-Markov process noun A generalization of the Markov chain in which the distribution of the amount of time that the process spends in a given state is permitted…
- skew normal distribution noun A continuous probability distribution that generalizes the normal distribution to allow for nonzero skewness.
- sojourn time noun The time spent in a state of a stochastic process.
- state space noun A (mathematical) space of all possible states of a system or process.
- stochastic process noun A function that maps elements of an index set to elements of a collection of random variables; historically, a collection of random…
- tree diagram noun A visual representation used to represent a probability space.
- unichain adj Of a Markov chain, consisting of a single recurrent class plus a possibly empty set of transient states.
- π-system noun A non-empty collection of subsets of a given set Ώ that is closed under non-empty finite intersections.