Mathematics and statistics

Erlang distribution

The Erlang distribution is a continuous probability distribution for the sum of k independent exponential random variables, modeling the waiting time until the k-th event of a Poisson process.

The Erlangen program is a research program in geometry set out by Felix Klein at the University of Erlangen in 1872, defining each geometry by the transformations under which its properties stay invariant.

Ernst Mally

Ernst Mally (1879–1944) was an Austrian philosopher at the University of Graz, a pupil of Alexius Meinong, who proposed the first formal system of deontic logic in 1926.

Error

Error is the difference between a measured or computed value and the value that would be obtained under ideal conditions, as distinct from a mistake.

Error exponent (hypothesis testing)

An error exponent in hypothesis testing is the constant E governing how fast a test's error probability decays exponentially, roughly as 2 to the power -nE, with sample size n.

Error function

The error function, also called the Gauss error function, is a special function defined by an integral of e^{-t^2}; it is closely related to the normal distribution.

Error statistics

Error statistics is a philosophy of statistical inference developed principally by philosopher Deborah G. Mayo, in which methods are judged by their probabilities of committing erroneous interpretations of data.

Error-state Kalman filter

The error-state Kalman filter (ESKF), or indirect Kalman filter, is a state-estimation algorithm whose Kalman filter estimates errors between the true state and a nominal state.

Errors and residuals

In statistics, an error is the difference between an observed value and the unknown true model value, while a residual is measured from a fitted model.

Errors-in-variables models

Errors-in-variables models are regression models that account for measurement error in predictor variables, correcting the biased, attenuated estimates ordinary least squares produces when covariates are observed with noise.

Essential spectrum

The essential spectrum of a linear operator, denoted σess(T), is the part of its spectrum unchanged by compact perturbations, with key applications to Schrödinger operators in quantum mechanics.

Essentially non-oscillatory scheme

An essentially non-oscillatory (ENO) scheme is a high-order numerical method for hyperbolic partial differential equations that avoids spurious oscillations near shocks via adaptive stencil selection.

Estimating equation

An estimating equation sets a function of the unknown parameter and observed data equal to zero; solving it yields the estimate, unifying least squares, maximum likelihood, and method of moments.

Estimating equations

An estimating equation is an equation in an unknown parameter whose solution is the estimate; it generalizes maximum likelihood and needs only the first two moments of the data.

Estimation

Estimation is the branch of statistics that uses sample data to assign values, or ranges of values, to unknown quantities called parameters, such as a population mean.

Estimation of distribution algorithm

An estimation of distribution algorithm (EDA) is a population-based optimization method that learns a probabilistic model of promising solutions and samples new candidates from it.

Estimator

An estimator is a statistic, a rule that computes a number from a random sample, used to estimate an unknown population parameter; the value it produces for one sample is the estimate.

Étale cohomology

Étale cohomology is a cohomology theory for algebraic varieties and schemes in which étale morphisms act as covers, developed by Grothendieck and Artin to prove the Weil conjectures, completed by Deligne in 1974.

Étale fundamental group

The étale fundamental group, also called the algebraic fundamental group, is an invariant of a scheme introduced by Alexander Grothendieck that classifies its finite étale covers as the topological fundamental group classifies covering spaces.

Étale morphism

An étale morphism, or étale map, is a morphism of schemes that is smooth of relative dimension 0, the analog of a local diffeomorphism or covering map in topology.

EU-SILC

EU-SILC (European Union Statistics on Income and Living Conditions) is the EU's annual household survey collecting comparable data on income, poverty, and living conditions since 2003.

Euclid (Εὐκλείδης)

Euclid, also known as Euclid of Alexandria (Εὐκλείδης), was a Greek mathematician active about 300 BC whose thirteen-book Elements became the model of rigorous mathematics for two millennia.

Euclid's Elements

Euclid's Elements (Greek: Stoicheia) is a 13-book mathematical treatise from the 3rd century BC that presents geometry, number theory, and proportion as a deductive system and became the model for mathematical writing.

Euclid's lemma

Euclid's lemma, also called Euclid's first theorem, states that a prime dividing a product of two integers must divide one factor, and it proves unique prime factorization.

Euclid's theorem

Euclid's theorem, on the infinitude of primes, states that there are infinitely many prime numbers; Euclid proved it around 300 BC as Proposition 20 of Book IX of the Elements.

Euclidean algorithm

The Euclidean algorithm, also called Euclid's algorithm, is a procedure for finding the greatest common divisor of two integers, described by Euclid around 300 BC.

Euclidean distance

Euclidean distance, or Pythagorean metric, is the ordinary straight-line distance between two points in Euclidean space, the square root of the sum of squared coordinate differences.

Euclidean division

Euclidean division, also called division with remainder, is the theorem that dividing one integer by a nonzero integer yields a unique quotient and remainder smaller than the divisor.

Euclidean domain

A Euclidean domain is an integral domain with a Euclidean norm allowing division with remainder, as in the integers, so the Euclidean algorithm computes greatest common divisors.