In mathematics, finite-dimensional distributions are a tool in the study of measures and stochastic processes. A lot of information can be gained by studying...

corresponding finite-dimensional distributions. Another approach involves defining a collection of random variables to have specific finite-dimensional distributions...

high-dimensional spaces that do not occur in low-dimensional settings such as the three-dimensional physical space of everyday experience. The expression...

\textstyle B} . For some finite integer k ≥ 1 {\displaystyle \textstyle k\geq 1} , we can give the finite-dimensional distribution of the homogeneous Poisson...

the Airy function. The process can be defined through its finite-dimensional distribution with a Fredholm determinant and the so-called extended Airy...

about the underlying distribution of the data being studied. Often these models are infinite-dimensional, rather than finite dimensional, as in parametric...

that guarantees that a suitably "consistent" collection of finite-dimensional distributions will define a stochastic process. It is credited to the English...

FEM to solve high-dimensional problems. To solve a problem, FEM subdivides a large system into smaller, simpler parts called finite elements. This is...

mixture weights. The number of components in a mixture distribution is often restricted to being finite, although in some cases the components may be countably...

and statistics, the discrete uniform distribution is a symmetric probability distribution wherein each of some finite whole number n of outcome values are...

theory and statistics, the beta-binomial distribution is a family of discrete probability distributions on a finite support of non-negative integers arising...

shape of the distribution. The beta distribution has been applied to model the behavior of random variables limited to intervals of finite length in a...

Mises–Fisher distribution on the N-dimensional sphere has the von Mises distribution as a special case. The Bingham distribution on the N-dimensional sphere...

As zero-dimensional objects, points are usually taken to be the fundamental indivisible elements comprising the space, of which one-dimensional curves...

Finite-difference time-domain (FDTD) or Yee's method (named after the Chinese American applied mathematician Kane S. Yee, born 1934) is a numerical analysis...

"pathological" distribution since both its expected value and its variance are undefined (but see § Moments below). The Cauchy distribution does not have finite moments...

random variable with finite mean and variance is itself a random variable—whose distribution converges to a normal distribution as the number of samples...

multivariate normal distribution, multivariate Gaussian distribution, or joint normal distribution is a generalization of the one-dimensional (univariate) normal...

(with no parameters); Its VC dimension is 0 since it cannot shatter even a single point. In general, the VC dimension of a finite classification model, which...

statistics, Student's t distribution (or simply the t distribution) t ν {\displaystyle t_{\nu }} is a continuous probability distribution that generalizes the...

The Wigner semicircle distribution, named after the physicist Eugene Wigner, is the probability distribution defined on the domain [−R, R] whose probability...

is finite-dimensional if its dimension is a natural number. Otherwise, it is infinite-dimensional, and its dimension is an infinite cardinal. Finite-dimensional...

tensor analysis with finite-dimensional vector spaces. When applied to vector spaces of functions (which are typically infinite-dimensional), dual spaces are...

earth (2-dimensional), the locations of imperfections in a material (3-dimensional), and the locations of trees in a forest (2-dimensional). The Poisson...

total size reading population has been normalized to 1. A typical finite-dimensional mixture model is a hierarchical model consisting of the following...

2), one-dimensional probability distributions. It can be used to test whether a sample came from a given reference probability distribution (one-sample...

measures, especially when the measure space has infinite dimension. See Finite-dimensional distribution Prokhorov's theorem Lévy–Prokhorov metric Weak convergence...

(1986). One-dimensional stable distributions. Providence, R.I.: American Mathematical Society. ISBN 0-8218-4519-5. "LandauDistribution—Wolfram Language...

f(x)=0} for all but a finite number of points x ∈ X , {\displaystyle x\in X,} then f {\displaystyle f} is said to have finite support. If the set X {\displaystyle...

{\displaystyle w} is no longer a finite-dimensional space R n {\displaystyle \mathbb {R} ^{n}} , but an infinite-dimensional function space. Moreover, by...