Mathematics and statistics

CRAN

CRAN, the Comprehensive R Archive Network, is the central curated archive and mirror network for the R statistical computing environment, founded in 1997 by Kurt Hornik and Friedrich Leisch.

Crank of a partition

The crank of a partition, also called Dyson's crank, is a partition statistic defined by Andrews and Garvan in 1988 that gives a combinatorial explanation of Ramanujan's three partition congruences.

Creative and productive sets

Creative and productive sets are linked classes of sets of natural numbers in computability theory, introduced by Emil Leon Post in 1944 to capture Gödel's first incompleteness theorem.

Credibility theory

Credibility theory is a statistical framework in actuarial science that blends a unit's own claims experience with collective class data to estimate future losses for insurance pricing.

Credible interval

A credible interval is an interval in which a parameter falls with a stated posterior probability given the data, the Bayesian analog of the confidence interval, used in FDA-regulated trials.

Critical exponent (dispersive PDE)

The critical exponent of a nonlinear dispersive PDE is the power at which the equation's scaling symmetry leaves a conserved Sobolev norm unchanged, organizing well-posedness and blow-up theory.

Critical point (mathematics)

In mathematics, a critical point, also called a critical number, is a point in a function's domain where the derivative is zero or fails to exist; local extrema must occur there.

Cross mapping (dynamical systems)

Cross mapping is a nonlinear time-series method that tests causal influence between variables; its main form, convergent cross mapping, was reported in Science in 2012.

The cross product, also called the vector product, is an operation on two vectors in three-dimensional space that produces a third vector perpendicular to both, with direction fixed by the right-hand rule.

Cross section (geometry)

A cross section in geometry is the two-dimensional shape made when a solid is cut through by a plane; the shape depends on the angle of the cut.

Cross-entropy

Cross-entropy is an information-theory quantity measuring the average code length needed to encode outcomes from a true distribution using a code designed for a different one; it also serves as a standard machine-learning training loss.

Cross-lagged panel analysis

Cross-lagged panel analysis is a longitudinal statistical method that models reciprocal relationships between variables measured repeatedly in the same units, widely used since the 1970s but contested for potentially spurious causal estimates.

Cross-lagged panel model

The cross-lagged panel model, or CLPM, is a longitudinal structural equation model that estimates reciprocal influences between two or more variables measured repeatedly over time.

Cross-lagged panel network

A cross-lagged panel network (CLPN) is a longitudinal statistical method combining cross-lagged panel regression with network analysis, estimating time-lagged relationships among variables such as psychological symptoms.

Cross-ratio

The cross-ratio, also called the double ratio or anharmonic ratio, is a number attached to four collinear points that stays unchanged under any projective transformation, playing the role length plays in Euclidean geometry.

Cross-sectional regression

Cross-sectional regression estimates relationships between variables measured across different units, such as firms, households, or stocks, at a single point in time, unlike time-series regression.

Cross-validation (statistics)

Cross-validation, also known as out-of-sample testing, is a statistical technique that estimates a model's predictive performance by repeatedly splitting data into training and test sets.

Crossed product of von Neumann algebras

The crossed product of von Neumann algebras, or Verschränktes Produkt, is a von Neumann algebra M ⋊ G built from M and a group action, analogous to the semidirect product.

Crossing number (graph theory)

The crossing number of a graph is the fewest edge crossings possible in any plane drawing of it, and it is 0 exactly when the graph is planar.

Crossover analysis

Crossover analysis is the statistical analysis of trials in which each subject receives a sequence of treatments in successive periods, so each subject serves as their own control.

Crossover study

A crossover study is a randomized clinical trial design in which every participant receives all compared treatments in randomized order, suited to chronic, stable conditions with short-lived treatment effects.

Cryptanalysis

Cryptanalysis, also called codebreaking, is the practice and mathematical study of defeating cryptographic protection without initial knowledge of the key, seeking attacks more efficient than brute force.

Cryptogram of Olivier Levasseur

The Cryptogram of Olivier Levasseur, or La Buse Cryptogram, is a 17-line pigpen cipher attributed to the French pirate, first published in 1934 and now considered likely a hoax.

Crystal base

A crystal base is a combinatorial structure attached to a representation of a quantum group, introduced in the early 1990s by Masaki Kashiwara and George Lusztig.

Cube

The cube, or regular hexahedron, is the Platonic solid bounded by six equal squares meeting at right angles, with 6 faces, 12 edges, and 8 vertices.

Cube (algebra)

The cube of a number, or cubic number, is the number multiplied by itself twice, written a3; cubing gives the volume of a cube with edge a.

Cube root

The cube root, also called the cubic root, of a number b is the number a with a³ = b; every real number has exactly one real cube root.

Cubic equation

A cubic equation, also known as a third-degree equation, is a polynomial equation of degree three whose general solution, found in sixteenth-century Italy, was the first advance beyond the quadratic formula.

Cubic function

A cubic function, also called a cubic polynomial, is a polynomial function of degree three, of the form f(x) = ax³ + bx² + cx + d.