Mathematics and statistics

Random permutation

A random permutation is a random ordering of n items in which every one of the n! possible orderings is equally likely, as in a fair shuffle.

Random permutation statistics studies quantities computed from a uniformly random permutation, such as cycles, descents, and inversions, including their distributions and limiting behavior as n grows.

Random regression model

A random regression model is a mixed statistical model expressing fixed and random effects as continuous functions of a covariate such as age or time.

Random regular graph

A random regular graph is a graph chosen uniformly at random from all graphs on n vertices with every vertex having the same degree d, the model G(n, d).

Random sample consensus

Random sample consensus (RANSAC) is an iterative method for fitting a mathematical model to data with many outliers, introduced by Fischler and Bolles of SRI International in 1981.

Random sampling

Random sampling selects units from a population by chance so every unit has a known probability of selection, allowing results to be generalized with calculable error.

Random tree

A random tree is a tree drawn from a probability distribution, such as a uniformly chosen combinatorial tree or the family tree of a Galton–Watson branching process.

Random variable

A random variable, also called a stochastic or aleatory variable, is a function that assigns a number to each outcome of a random experiment, formalized by Kolmogorov in 1933.

Random walk

A random walk, also called a drunken walk, is a stochastic process describing a path formed by successive random steps, used to model diffusion and fluctuation.

Random-access machine

A random-access machine (RAM) is an abstract model of computation: a program operating on an array of registers, any of which can be read or written directly by index.

Random-effects meta-analysis

Random-effects meta-analysis is a statistical method for combining effect estimates from multiple studies assumed to vary, following a distribution with a mean and a between-study variance.

Randomization inference

Randomization inference, also known as permutation inference, is a statistical method for testing treatment effects in experiments by computing a test statistic's distribution over all possible random assignments, requiring no distributional assumptions.

Randomization test

A randomization test is a statistical significance test that evaluates a treatment effect by repeatedly reassigning group labels at random, giving exact Type I error control without distributional assumptions.

Randomized block design

A randomized block design is a statistical experimental design that groups similar units into blocks and randomizes treatments within each block, removing block-to-block variation from experimental error.

Randomized rounding

Randomized rounding is a technique in combinatorial optimization that turns a fractional linear programming solution into an integer one, introduced by Raghavan and Thompson in 1987.

Randomized singular value decomposition

The randomized singular value decomposition (randomized SVD, or RSVD) is a numerical linear algebra algorithm that computes an approximate truncated SVD of a large matrix using random sampling.

Randomness

Randomness is the absence of exact predictability in the outcome of a process, modeled by assigning probabilities to each possible outcome and quantified by entropy.

Randomness test

A randomness test is a statistical procedure judging whether an ordered data sequence was produced randomly, detecting trends, oscillation, and autocorrelation; common examples include the Wald–Wolfowitz runs test.

Range (statistics)

The range in statistics is a measure of dispersion, the difference between the largest and smallest values in a data set, used mainly in quality control charts.

Rank (linear algebra)

The rank of a matrix is the dimension of the space spanned by its columns, equivalently its rows, equal to the number of pivots after row reduction.

Rank correlation

Rank correlation is a family of statistics that measures association between two variables by comparing ranks, with Spearman's ρ and Kendall's τ as the standard coefficients.

Rank of a partition

The rank of a partition is a statistic introduced by Freeman Dyson in 1944, defined as the largest part minus the number of parts, explaining Ramanujan's congruences.

Rank reduction (statistics)

Rank reduction is a statistical technique that approximates a data or parameter matrix by one of lower rank, minimizing squared error; in multivariate regression it appears as reduced-rank regression, introduced by T. W. Anderson in 1951.

Rank regression

Rank regression is a nonparametric regression method that fits models to the ranks of the data instead of raw values, reducing sensitivity to outliers and distributional assumptions.

Rank-into-rank cardinal

A rank-into-rank cardinal is the critical point of a nontrivial elementary embedding from some rank into itself, a hypothesis at the top of the large cardinal hierarchy in set theory.

Rank–nullity theorem

The rank–nullity theorem, also called the dimension theorem, is a linear algebra result stating that rank plus nullity equals the dimension of the map's domain.

Ranked set sampling

Ranked set sampling is a sampling design for estimating a population mean in which units are ranked cheaply before measurement, introduced by McIntyre in 1952.

Rao bound

The Rao bound, proved by the Indian statistician C. R. Rao in 1947, is a lower bound on the run size of any orthogonal array of given strength.

Rao–Blackwell theorem

The Rao–Blackwell theorem, also called the Rao–Blackwell–Kolmogorov theorem, is a result in statistical estimation theory proved by C. R. Rao and David Blackwell in 1945 and 1947.