Mathematics and statistics

Discrete Mathematics (journal)

Discrete Mathematics is a peer-reviewed mathematics journal published by Elsevier that covers combinatorics and graph theory; it was founded in 1971 by North-Holland in Amsterdam.

Discrete space

A discrete space is a set equipped with the discrete topology, the finest topology possible, in which every subset of the set is open and every point is isolated.

Discrete spectrum (functional analysis)

The discrete spectrum of a self-adjoint operator is the part of its spectrum made of isolated eigenvalues of finite multiplicity, with the rest the essential spectrum.

Discrete time and continuous time

Discrete time and continuous time, also called discrete-time and continuous-time variables, are the two ways a system's state can be indexed in time, by difference or differential equations.

Discrete uniform distribution

The discrete uniform distribution is a probability distribution giving equal probability to each of a finite set of equally likely outcomes, such as a fair die roll.

Discrete valuation ring

A discrete valuation ring (DVR) is a principal ideal domain with exactly one nonzero prime ideal; examples include the power series ring k[[t]] and the integers localized at a prime.

The discrete wavelet transform (DWT) is a linear transform that decomposes a discrete signal into wavelet coefficients carrying both scale and position information, computed by a fast filter-bank algorithm.

Discretization

Discretization, also called discretizing, replaces a continuous mathematical problem with a finite discrete counterpart a computer can solve, turning differential equations into algebraic systems and signals into samples.

Discriminant

The discriminant is a quantity computed from the coefficients of a polynomial or quadratic form that vanishes exactly when the object degenerates, as when two roots coincide.

Discriminant analysis

Discriminant analysis is a family of supervised statistical classification methods that model differences between known groups and assign new observations to the group they most likely belong to.

Disdyakis triacontahedron

The disdyakis triacontahedron, also called the hexakis icosahedron, is a Catalan solid with 120 scalene triangular faces, the most of any Catalan solid, and serves as the shape of the 120-sided die.

Disease mapping

Disease mapping is the set of statistical methods for estimating and displaying how disease risk varies across small geographic areas, typically by smoothing unstable local rates.

Disease progression modeling

Disease progression modeling is a biostatistical method using mathematical models to describe a disease's trajectory over time and separate natural progression from drug effects in drug development.

Disjoint sets

Disjoint sets, also called mutually exclusive sets, are sets that share no elements, so their intersection is empty; the concept underlies partitions and counting rules.

Displacement (geometry)

Displacement, also called a displacement vector, is the change in position of a point, a vector with both magnitude and direction; in geometry it defines a translation.

Disproportionality analysis

Disproportionality analysis is a family of statistical methods, including PRR, ROR, IC, and EBGM, used to detect higher-than-expected reporting of drug–adverse-event pairs in spontaneous-reporting databases.

Dissolution testing

Dissolution testing is a laboratory procedure that measures the rate and extent to which a drug substance is released from a dosage form, such as a tablet or capsule, under controlled conditions.

Distance correlation

Distance correlation is a measure of statistical dependence between two random vectors, introduced by Székely, Rizzo, and Bakirov in 2007, that is zero if and only if they are independent.

Distance from a point to a line

The distance from a point to a line, also called the perpendicular distance, is the length of the shortest segment joining the point to the line, minimized by the perpendicular.

Distance geometry

Distance geometry is a mathematical method that determines possible three-dimensional structures of molecules from a set of distances between pairs of points, mainly from NMR data.

Distance matrix

A distance matrix is a square matrix recording the pairwise distances between elements of a finite set, with a symmetric, zero-diagonal form when the distance is a metric.

Distance sampling

Distance sampling is a suite of survey methods, built on line and point transects, that estimates animal or plant density and abundance from measured distances to detected individuals.

Distance-regular graph

A distance-regular graph is a connected graph where, for any two vertices at a given distance, the counts of neighbors at each distance depend only on that distance.

Distributed algorithm

A distributed algorithm is a concurrent algorithm executed by multiple processors that lack shared memory and a common clock, coordinating only by message passing across a network.

Distributed lag model

A distributed lag model is a time series regression that estimates a predictor's effect on an outcome as spread over several past values, with coefficients called lag weights.

Distributed lag non-linear model

The distributed lag non-linear model (DLNM) is a regression framework estimating non-linear exposure–outcome relationships and how they unfold over time lags, developed for environmental epidemiology.

Distribution (mathematics)

In mathematics, a distribution, also known as a Schwartz distribution or generalized function, is an object that extends the notion of function, making differentiation possible for every element.

Distribution fitting

Distribution fitting is the statistical method of selecting a candidate probability distribution family, estimating its parameters from data, and assessing how well the fitted distribution reproduces the data.

Distributional regression

Distributional regression is a class of statistical models that estimates the full conditional distribution of a response given explanatory variables, capturing variance, skewness, and tails.