Borel distribution information

The Borel distribution is a discrete probability distribution, arising in contexts including branching processes and queueing theory. It is named after...

complement. Borel sets are named after Émile Borel. For a topological space X, the collection of all Borel sets on X forms a σ-algebra, known as the Borel algebra...

cases include: The Gibbs distribution The Maxwell–Boltzmann distribution The Borel distribution The discrete phase-type distribution, a generalization of...

Émile Borel Borel algebra, operating on Borel sets, named after Émile Borel, also: Borel measure, the measure on a Borel algebra Borel distribution, a discrete...

in measure theory, a Borel measure on a topological space is a measure that is defined on all open sets (and thus on all Borel sets). Some authors require...

motivates the distribution's name. This distribution can be generalized to more complicated sets than intervals. Let S {\displaystyle S} be a Borel set of positive...

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

The concept of the conditional distribution of a continuous random variable is not as intuitive as it might seem: Borel's paradox shows that conditional...

can be defined. Normally, a particular such sigma-algebra is used, the Borel σ-algebra, which allows for probabilities to be defined over any sets that...

of an unknown distribution from a realization of the sequence, but also any feature of the probability distribution. By applying Borel's law of large numbers...

events { X n = 1 } {\displaystyle \{X_{n}=1\}} are independent, second Borel Cantelli Lemma ensures that P ( lim sup n { X n = 1 } ) = 1 {\displaystyle...

subsets of G {\displaystyle G} is called the Borel algebra. An element of the Borel algebra is called a Borel set. If g {\displaystyle g} is an element of...

{\displaystyle \mathbb {R} ^{n}} with the Borel sets as measurable subsets) has as probability distribution the measure X∗P on ( X , A ) {\displaystyle...

_{x}} is Borel measurable, in the sense that x ↦ μ x ( B ) {\displaystyle x\mapsto \mu _{x}(B)} is a Borel-measurable function for each Borel-measurable...

elliptical distribution is any member of a broad family of probability distributions that generalize the multivariate normal distribution. Intuitively...

the use of the "monkey metaphor" is that of French mathematician Émile Borel in 1913, but the first instance may have been even earlier. Jorge Luis Borges...

finite-dimensional distribution of the homogeneous Poisson point process by first considering a collection of disjoint, bounded Borel (measurable) sets...

probability distribution on ( R , B ) {\displaystyle \left(\mathbb {R} ,{\mathfrak {B}}\right)} (where B {\displaystyle {\mathfrak {B}}} is the standard Borel set...

measure is a Borel measure on finite-dimensional Euclidean space R n {\displaystyle R^{n}} , closely related to the normal distribution in statistics...

function, nearest neighbor distance distribution, nearest-neighbor distribution function or nearest neighbor distribution is a mathematical function that...