Sometimes, a value of a Gaussian random function deviates from its expected value by several standard deviations. This is a large deviation. Though rare in...

peak, and c (the standard deviation, sometimes called the Gaussian RMS width) controls the width of the "bell". Gaussian functions are often used to represent...

Brownian motion Varadhan's lemma Extreme value theory Large deviations of Gaussian random functions S.R.S. Varadhan, Asymptotic probability and differential...

many) random variables, and as such, it is a distribution over functions with a continuous domain, e.g. time or space. The concept of Gaussian processes...

Gauss–Markov process Gaussian process Gaussian random field Gaussian isoperimetric inequality Large deviations of Gaussian random functions Girsanov's theorem...

Large deviations of Gaussian random functions / Gau Rate function Schilder's theorem / Gau Tilted large deviation principle Varadhan's lemma Random graph...

distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability...

{E[S_{n}^{2}]}}=\sigma {\sqrt {n}}.} But for the Gaussian random walk, this is just the standard deviation of the translation distance's distribution after...

In statistics, a Gaussian random field (GRF) is a random field involving Gaussian probability density functions of the variables. A one-dimensional GRF...

the tails of a Gaussian. This property gives subgaussian distributions their name. Often in analysis, we divide an object (such as a random variable)...

Laplace principle (large deviations theory) LaplacesDemon – software Large deviations theory Large deviations of Gaussian random functions LARS – see least-angle...

the law of large numbers is a mathematical law that states that the average of the results obtained from a large number of independent random samples...

statistics, for non-negative real values of x, the error function has the following interpretation: for a real random variable Y that is normally distributed...

sample of values of some random variable), or of an estimator (i.e., a mathematical function mapping a sample of data to an estimate of a parameter of the...

a Gaussian random polytope. A similar result holds for the number of vertices (of the Gaussian polytope), the number of edges, and in fact, faces of all...

the limitations of the Gaussian copula and of copula functions more generally, specifically the lack of dependence dynamics. The Gaussian copula is lacking...

various categories, which include random walks, martingales, Markov processes, Lévy processes, Gaussian processes, random fields, renewal processes, and...

weighted sum of exponential densities. Hypoexponential distribution – the distribution of a general sum of exponential random variables. exGaussian distribution...

algorithm for mixtures of Gaussian distributions via an iterative refinement approach employed by both k-means and Gaussian mixture modeling. They both...

probability distribution. Random matrix theory (RMT) is the study of properties of random matrices, often as they become large. RMT provides techniques...

generally unique, apart from the Gaussian case, and there may be alternatives. The distribution of the product of a random variable having a uniform distribution...

the standard deviation of the Student t-distribution. T-distributions are slightly different from Gaussian, and vary depending on the size of the sample...

posterior mode of a Gaussian process regression. Kernel regression estimates the continuous dependent variable from a limited set of data points by convolving...

probability that a normal (Gaussian) random variable will obtain a value larger than x {\displaystyle x} standard deviations. Equivalently, Q ( x ) {\displaystyle...

large values of λ include rejection sampling and using Gaussian approximation. Inverse transform sampling is simple and efficient for small values of...

the sum of the squares of n independent Gaussian random variables. It is a special case of the Gamma distribution, and it is used in goodness-of-fit tests...

identically distributed real random variables with the common cumulative distribution function F(t). Then the empirical distribution function is defined as F ^ n...

correlation between two sets of data. It is the ratio between the covariance of two variables and the product of their standard deviations; thus, it is essentially...

criterion functions). The theorem is valid for all regions of acceptability and all Gaussian distributions. It may be used by cyclic repetition of random variation...

causal or not, between two random variables or bivariate data. Although in the broadest sense, "correlation" may indicate any type of association, in statistics...