Random variable with multiple component dimensions
Part of a series on statistics
Probability theory
Probability
Axioms
Determinism
System
Indeterminism
Randomness
Probability space
Sample space
Event
Collectively exhaustive events
Elementary event
Mutual exclusivity
Outcome
Singleton
Experiment
Bernoulli trial
Probability distribution
Bernoulli distribution
Binomial distribution
Exponential distribution
Normal distribution
Pareto distribution
Poisson distribution
Probability measure
Random variable
Bernoulli process
Continuous or discrete
Expected value
Variance
Markov chain
Observed value
Random walk
Stochastic process
Complementary event
Joint probability
Marginal probability
Conditional probability
Independence
Conditional independence
Law of total probability
Law of large numbers
Bayes' theorem
Boole's inequality
Venn diagram
Tree diagram
v
t
e
For broader coverage of this topic, see Multivariate statistics.
In probability, and statistics, a multivariate random variable or random vector is a list or vector of mathematical variables each of whose value is unknown, either because the value has not yet occurred or because there is imperfect knowledge of its value. The individual variables in a random vector are grouped together because they are all part of a single mathematical system — often they represent different properties of an individual statistical unit. For example, while a given person has a specific age, height and weight, the representation of these features of an unspecified person from within a group would be a random vector. Normally each element of a random vector is a real number.
Random vectors are often used as the underlying implementation of various types of aggregate random variables, e.g. a random matrix, random tree, random sequence, stochastic process, etc.
More formally, a multivariate random variable is a column vector (or its transpose, which is a row vector) whose components are scalar-valued random variables on the same probability space as each other, , where is the sample space, is the sigma-algebra (the collection of all events), and is the probability measure (a function returning each event's probability).
and 28 Related for: Multivariate random variable information
probability, and statistics, a multivariaterandomvariable or random vector is a list or vector of mathematical variables each of whose value is unknown...
real-valued randomvariables, each of which clusters around a mean value. The multivariate normal distribution of a k-dimensional random vector X = (...
and analysis of more than one outcome variable, i.e., multivariaterandomvariables. Multivariate statistics concerns understanding the different aims...
two variables. The variables may be two columns of a given data set of observations, often called a sample, or two components of a multivariaterandom variable...
distribution, and such functions exist for either scalar or multivariaterandomvariables whose domain is discrete. A probability mass function differs...
A randomvariable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which...
In statistics, sometimes the covariance matrix of a multivariaterandomvariable is not known but has to be estimated. Estimation of covariance matrices...
density function together with a multivariate probability mass function. In the special case of continuous randomvariables, it is sufficient to consider...
specify the distribution of multivariaterandomvariables. The cumulative distribution function of a real-valued randomvariable X {\displaystyle X} is the...
population (sampling without replacement from a finite population). A randomvariable X {\displaystyle X} follows the hypergeometric distribution if its...
calculation of the sum of normally distributed randomvariables is an instance of the arithmetic of randomvariables. This is not to be confused with the sum...
called multivariate. A univariate distribution gives the probabilities of a single randomvariable taking on various different values; a multivariate distribution...
is a type of continuous probability distribution for a real-valued randomvariable. The general form of its probability density function is f ( x ) =...
redirects to Multivariate probit model MultivariaterandomvariableMultivariate stable distribution Multivariate statistics Multivariate Student distribution –...
case there are k+p dependent variables whose linear combination follows a multivariate normal distribution, multivariate variance-covariance matrix homogeneity...
multivariate model can contain both discrete and continuous variables. For instance, a simple mixed multivariate model could have a discrete variable...
Heaviside step function.[citation needed] Degeneracy of a multivariate distribution in n randomvariables arises when the support lies in a space of dimension...
variability of two randomvariables. The sign of the covariance, therefore, shows the tendency in the linear relationship between the variables. If greater values...
the independent variable is manipulated. In data mining tools (for multivariate statistics and machine learning), the dependent variable is assigned a role...
calculus (also known as multivariate calculus) is the extension of calculus in one variable to calculus with functions of several variables: the differentiation...
randomvariables having two other known distributions. Given two statistically independent randomvariables X and Y, the distribution of the random variable...
parameter. The distribution is supported on the interval [0, ∞). If a randomvariable X has this distribution, we write X ~ Exp(λ). The exponential distribution...
the randomvariable Y = a T X {\displaystyle Y=a^{T}X} should have a univariate Cauchy distribution. The characteristic function of a multivariate Cauchy...
could be well modeled by a Poisson distribution.: 23-25 . A discrete randomvariable X is said to have a Poisson distribution, with parameter λ > 0 , {\displaystyle...
in a longitudinal study). Multivariate analysis of variance (MANOVA) is used when there is more than one response variable. Balanced experiments (those...
is any statistical relationship, whether causal or not, between two randomvariables or bivariate data. Although in the broadest sense, "correlation" may...
probability, multivariate Laplace distributions are extensions of the Laplace distribution and the asymmetric Laplace distribution to multiple variables. The...
Global Information
