(mathematics) Pertaining to values or properties approached at infinity.

(statistics) A directed acyclic graph whose vertices represent random variables and whose directed edges represent conditional dependencies. Each random variable can fall into any of at least two mutually disjoint states, and has a probability function which takes as inputs the states of its parent nodes and returns as output the probability of being in a certain state for a given combination of the states of its parent nodes. A node without parent nodes just has an unconditioned probability of being in some given state.

A law concerning the frequency distribution of digits in much real-world data, where the number 1 occurs as the leading digit about 30% of the time, and the expected distribution for digits beyond the first approaches a uniform distribution.

(statistics) A discrete probability distribution that represents the result of a single trial, taking value 1 with "success" probability p and value 0 with "failure" probability q=1-p.

(probability, statistics) Any of a family of continuous probability distributions defined on the interval [0, 1] whose shape is parametrised by two positive parameters, denoted α and β, which appear as exponents in the associated random variable.

(mathematics, of a category) Both complete and cocomplete.

(probability theory) The mathematics problem that concerns the probability there exist two people in a random group who share a birthday.

(mathematics) Any of a set of constraints that limit the solutions of a differential equation

(more formally) the entire sample space (which by definition has measure 1 and probability 1); said sample space with the exclusion of, at most, a set of measure 0 (thus retaining measure 1).

(statistics) A lower bound on the variance of estimators of a deterministic parameter; a generalization of the Cramér-Rao bound, it is both tighter and more widely applicable, but usually harder to compute.

The use of the Kahan summation algorithm.

(probability theory) The probability distribution of a random variable given the known outcome of another random variable.

(statistics) A variable that has a continuous distribution function, such as temperature.

(mathematics, probability theory) 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

(mathematics, statistics) A sigmoid function giving the probability that a measurement, under the influence of normally distributed errors with standard deviation, is within a certain distance from the mean value.

(statistics, probability) A probability distribution of the ratio of two variables, each with a chi-square distribution; used in analysis of variance, especially in the significance testing of a correlation coefficient (R squared).

(statistics) A measure of the amount of information that an observable random variable X carries about an unknown parameter θ of a distribution that models X. Formally, it is the variance of the score, or the expected value of the observed information.

(statistics) the normal distribution.

(statistics) normal distribution.

Either of two slightly different discrete probability distributions, each based on repetitions of a trial with "success" probability p: (1) the number X of trials required to obtain one success, or (2) the number Y = X − 1 of failed trials before the first success.

(statistics, economics) A measure of the inequality of a statistical distribution, ranging from 0 (total equality) to 1 (maximal inequality), used in various disciplines but especially in economics to compare incomes or wealth.

(mathematics) An element in a function's domain where the function assumes its highest value.

(set theory, order theory) A pair of collections of integer sequences such that there is no integer sequence lying between the two.

A statistical Markov model in which the system being modelled is assumed to be a Markov process with unobserved (hidden) states.

(mathematics) Constant.

(probability) In Bayesian probability, a non-informative (objective) prior distribution for a parameter space; it is proportional to the square root of the determinant of the Fisher information matrix.

(statistics, biology) A class of continuous probability distributions developed in 1943 by the English statistician and biologist Ronald Fisher to fit some particular species distribution data sets.

(algebra) A sum that is a logical OR of a set of variables where each individual variable only appears once in the sum, either in complemented or uncomplemented form, so that the value of the sum becomes 0.

(mathematics) Any function of multiple variables that satisfies certain properties and yields a number representative of its arguments; or, the number so yielded; a measure of central tendency.

(mathematical analysis) A lower bound of a set which is also an element of that set.

(statistics) A discrete probability distribution of the number of successes in a sequence of independent and identically distributed Bernoulli trials before a specified (non-random) number of failures (denoted r) occurs.

(probability theory) The result of a random trial. An element of a sample space.

(mathematics) Of or pertaining to the Poisson distribution.

(probability) An upper bound on the variance of any bounded probability distribution.

(probability theory) Any function whose integral over a set gives the probability that a random variable has a value in that set

(statistics) A distribution of all possible values of a random variable together with an indication of their probabilities.

Graph paper with vertical and horizontal rules, the latter spaced evenly and the former according to a scale that allows a plotted probability curve — usually that of a normal distribution — to appear linear.

(probability theory, statistics) A discrete probability distribution where a random variate has a 50% chance of being +1 and a 50% chance of being -1.

(statistics, probability theory) A sequence of identically distributed random variables.

(statistics) The probability distribution of the magnitude of a circular bivariate normal random variable with potentially non-zero mean.

(differential equations) Able to be brought to a form where all occurrences of the dependent and the independent variable are on opposite sides of the equal sign.

(mathematical analysis, of a function) The highest order of derivative (the differentiability class) over a given domain.

(mathematics) A branch of mathematics that operates on stochastic processes.

(statistics) A distribution that arises when the population standard deviation is unknown and has to be estimated from the data.

(mathematics) A stochastic process for which the conditional expectation of future values given the sequence of all prior values is superior or equal to its current value.

(countable, statistics) Any of various generalizations of a distribution, especially a common distribution that results from applying a single mapping to any distribution from a body of source distributions, which forms the basis of encryption used in the superdistribution of digital products.

(mathematics) Having a value that is independent of dimension

(mathematics) The problem of the unknown cost of rounding transcendental functions.

(mathematics, stochastic processes) A square matrix whose rows consist of nonnegative real numbers, with each row summing to 1. Used to describe the transitions of a Markov chain; its element in the ith row and jth column describes the probability of moving from state i to state j in one time step.

(statistics) A continuous, symmetric probability distribution defined in terms of its quantile function, typically used to identify an appropriate distribution.

(game theory) A mathematical function that assigns a real number to every element of the outcome space in a way that captures the agent's preferences over both simple and compound lotteries.

(signal processing) An approximation to the likelihood function of a stationary Gaussian time series.

(statistics) A certain discrete probability distribution.

The fact that many types of data studied in the physical and social sciences can be approximated with a Zipfian distribution.