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Random variable with multiple component dimensions
probability and statistics, a multivariate random variable or random vector is a list or vector of mathematical variables each of whose value is unknown
Multivariate_random_variable
Generalization of the one-dimensional normal distribution to higher dimensions
real-valued random variables, each of which clusters around a mean value. The multivariate normal distribution of a k-dimensional random vector X = (
Multivariate normal distribution
Multivariate_normal_distribution
Variable representing a random phenomenon
A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which
Random_variable
Simultaneous observation and analysis of more than one outcome variable
and analysis of more than one outcome variable, i.e., multivariate random variables. Multivariate statistics concerns understanding the different aims
Multivariate_statistics
Discrete-variable probability distribution
distribution, and such functions exist for either scalar or multivariate random variables whose domain is discrete. A probability mass function differs
Probability_mass_function
Topics referred to by the same term
division algorithm Multivariate optical computing Multivariate analysis Multivariate random variable Multivariate regression Multivariate statistics Univariate
Multivariate
Probability that random variable X is less than or equal to x
specify the distribution of multivariate random variables. The cumulative distribution function of a real-valued random variable X {\displaystyle X} is the
Cumulative distribution function
Cumulative_distribution_function
Numerical measure of a statistical relationship between variables
two variables. The variables may be two columns of a given data set of observations, often called a sample, or two components of a multivariate random variable
Correlation_coefficient
Multivariable generalization of the Student's t-distribution
the multivariate t-distribution (or multivariate Student distribution) is a multivariate probability distribution. It is a generalization to random vectors
Multivariate_t-distribution
Probability distribution
and Random Processes (2nd ed.). Academic Press. p. 128. ISBN 9780128010358. Richard Arnold Johnson; Dean W. Wichern (2007). Applied Multivariate Statistical
Exponential_distribution
Discrete probability distribution
population (sampling without replacement from a finite population). A random variable X {\displaystyle X} follows the hypergeometric distribution if its
Hypergeometric_distribution
Probability distribution
the random variable Y = a T X {\displaystyle Y=a^{T}X} should have a univariate Cauchy distribution. The characteristic function of a multivariate Cauchy
Cauchy_distribution
Fourier transform of the probability density function
notion of characteristic functions generalizes to multivariate random variables and more complicated random elements. The argument of the characteristic function
Characteristic function (probability theory)
Characteristic_function_(probability_theory)
Types of numerical variables in mathematics
multivariate model can contain both discrete and continuous variables. For instance, a simple mixed multivariate model could have a discrete variable
Continuous or discrete variable
Continuous_or_discrete_variable
Statistics concept
In statistics, sometimes the covariance matrix of a multivariate random variable is not known but has to be estimated. Estimation of covariance matrices
Estimation of covariance matrices
Estimation_of_covariance_matrices
Mathematical function for the probability a given outcome occurs in an experiment
called multivariate. A univariate distribution gives the probabilities of a single random variable taking on various different values; a multivariate distribution
Probability_distribution
Probability distribution
random variables having two other known distributions. Given two statistically independent random variables X and Y, the distribution of the random variable
Distribution of the product of two random variables
Distribution_of_the_product_of_two_random_variables
Probability distribution
random variable is independent of itself, then it is almost surely constant. Degeneracy of a multivariate distribution in n random variables arises when
Degenerate_distribution
Discrete probability distribution
kicks could be well modeled by a Poisson distribution.. A discrete random variable X is said to have a Poisson distribution with parameter λ > 0 {\displaystyle
Poisson_distribution
Procedure for comparing multivariate sample means
case there are k+p dependent variables whose linear combination follows a multivariate normal distribution, multivariate variance-covariance matrix homogeneity
Multivariate analysis of variance
Multivariate_analysis_of_variance
Type of probability distribution
{\displaystyle p(Y)} Given random variables X , Y , … {\displaystyle X,Y,\ldots } , that are defined on the same probability space, the multivariate or joint probability
Joint probability distribution
Joint_probability_distribution
Topics referred to by the same term
element in a set, that element is unchanged Neutral vector, a multivariate random variable that exhibits a particular type of statistical independence (Dirichlet
Neutral
Collection of statistical models
in a longitudinal study). Multivariate analysis of variance (MANOVA) is used when there is more than one response variable. Balanced experiments (those
Analysis_of_variance
Matrix-valued random variable
mathematical physics, a random matrix is a matrix-valued random variable—that is, a matrix in which some or all of its entries are sampled randomly from a probability
Random_matrix
Apparent lack of pattern or predictability in events
probabilities of the events. Random variables can appear in random sequences. A random process is a sequence of random variables whose outcomes do not follow
Randomness
Extension to cover cases with multiple dependent variables
Multivariate analysis of covariance (MANCOVA) is an extension of analysis of covariance (ANCOVA) methods to cover cases where there is more than one dependent
Multivariate analysis of covariance
Multivariate_analysis_of_covariance
distribution multivariate analysis multivariate kernel density estimation multivariate random variable A vector whose components are random variables on the
Glossary of probability and statistics
Glossary_of_probability_and_statistics
Probability distribution
is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is f ( x ) =
Normal_distribution
Rule for estimating the mean of a dataset
{\theta }}:=(\theta _{1},\theta _{2},\dots \theta _{m})} for a multivariate random variable Y := ( Y 1 , Y 2 , … Y m ) {\displaystyle {\boldsymbol {Y}}:=(Y_{1}
James–Stein_estimator
Probability distribution
probability, multivariate Laplace distributions are extensions of the Laplace distribution and the asymmetric Laplace distribution to multiple variables. The
Multivariate Laplace distribution
Multivariate_Laplace_distribution
Concept in mathematical modeling, statistical modeling and experimental sciences
In data mining tools (for multivariate statistics and machine learning), the dependent variable is called target variable (or in some tools as label
Dependent and independent variables
Dependent_and_independent_variables
Calculus of functions of several variables
calculus (also known as multivariate calculus) is the extension of calculus in one variable to functions of several variables: the differentiation and
Multivariable_calculus
Probability distribution
uniform base measure and a 1 / x {\displaystyle 1/x} base measure) for a random variable X for which E[X] = αθ = α/β is fixed and greater than zero, and E[ln
Gamma_distribution
Type of probability distribution
Hotelling's T-squared distribution (T2), proposed by Harold Hotelling, is a multivariate probability distribution that is tightly related to the F-distribution
Hotelling's T-squared distribution
Hotelling's_T-squared_distribution
Probability distribution
continuous probability distribution of a random variable whose logarithm is normally distributed. Thus, if the random variable X is log-normally distributed, then
Log-normal_distribution
Bayesian approach to multivariate linear regression
predicted outcome is a vector of correlated random variables rather than a single scalar random variable. A more general treatment of this approach can
Bayesian multivariate linear regression
Bayesian_multivariate_linear_regression
Statistical distance measure
more variable scores. Even for normal distributions, a point can be a multivariate outlier even if it is not a univariate outlier for any variable (consider
Mahalanobis_distance
Continuous probability distribution
a continuous probability distribution. It models a broad range of random variables, largely in the nature of a time to failure or time between events
Weibull_distribution
Broad concept generalizing scalars in mathematics and physics
one. Random vector or multivariate random variable, in statistics, a set of real-valued random variables that may be correlated. However, a random vector
Vector (mathematics and physics)
Vector_(mathematics_and_physics)
generalized variance is a scalar value which generalizes variance for multivariate random variables. It was introduced by Samuel S. Wilks. The generalized variance
Generalized_variance
Constant random variable Expected value Jensen's inequality Variance Standard deviation Geometric standard deviation Multivariate random variable Joint probability
List_of_probability_topics
Notion in statistics
is a way of measuring the amount of information that an observable random variable X carries about an unknown parameter θ of a distribution that models
Fisher_information
Measure of covariance of components of a random vector
refer to random vectors, and Roman subscripted X i {\displaystyle X_{i}} and Y i {\displaystyle Y_{i}} are used to refer to scalar random variables. If the
Covariance_matrix
Statistical measure of how far values spread from their average
as the expected value of the squared deviation from the mean of a random variable. The standard deviation is the square root of the variance. Technically
Variance
Set of random variables
physics and probability, a Markov random field (MRF), Markov network or undirected graphical model is a set of random variables having a Markov property described
Markov_random_field
Statistical relationship
statistics, correlation is a type of statistical relationship between two random variables or bivariate data. It usually refers to the extent to which a pair
Correlation
Middle quantile of a data set or probability distribution
occurs in the setting where we seek to estimate a random variable X {\displaystyle X} from a random variable Y {\displaystyle Y} , which is a noisy version
Median
Statistical distribution for dependence between random variables
statistics, a copula is a multivariate cumulative distribution function for which the marginal probability distribution of each variable is uniform on the interval [0
Copula_(statistics)
Probability distribution and special case of gamma distribution
of the squares of k {\displaystyle k} independent standard normal random variables. The chi-squared distribution χ k 2 {\displaystyle \chi _{k}^{2}} is
Chi-squared_distribution
Concept in probability theory and statistics
correlation if the random variables are jointly distributed as the multivariate normal, other elliptical, multivariate hypergeometric, multivariate negative hypergeometric
Partial_correlation
Statistical modeling method
model with two or more explanatory variables is a multiple linear regression. This term is distinct from multivariate linear regression, which predicts
Linear_regression
not look random, but it satisfies the definition of random variable. This is useful because it puts deterministic variables and random variables in the
List of probability distributions
List_of_probability_distributions
redirects to Multivariate probit model Multivariate random variable Multivariate stable distribution Multivariate statistics Multivariate Student distribution –
List_of_statistics_articles
Thematic map visualizing multiple variables
A bivariate map or multivariate map is a type of thematic map that displays two or more variables on a single map by combining different sets of symbols
Multivariate_map
Measure of variation in statistics
the lowercase Greek letter σ (sigma). The standard deviation of a random variable, sample, statistical population, data set or probability distribution
Standard_deviation
Statistical model
econometrics, a random effects model, also called a variance components model, is a statistical model where the model effects are random variables. It is a kind
Random_effects_model
Statistical linear model
a matrix with series of multivariate measurements (each column being a set of measurements on one of the dependent variables), X is a matrix of observations
General_linear_model
Measure of dependence between two variables
the mutual information (MI) of two random variables is a measure of the mutual dependence between the two variables. More specifically, it quantifies the
Mutual_information
Statistical property
In statistics, a sequence of random variables is homoscedastic (/ˌhoʊmoʊskəˈdæstɪk/) if all its random variables have the same finite variance; this is
Homoscedasticity and heteroscedasticity
Homoscedasticity_and_heteroscedasticity
Distributions in probability theory
statistics, the Dirichlet-multinomial distribution is a family of discrete multivariate probability distributions on a finite support of non-negative integers
Dirichlet-multinomial distribution
Dirichlet-multinomial_distribution
Measure of the joint variability
variability of two random variables. The sign of the covariance shows the tendency in the linear relationship between the variables. Covariance is positive
Covariance
Class of statistical tests
well-modeled by a normal distribution and to compute how likely it is for a random variable underlying the data set to be normally distributed. More precisely
Normality_test
Parameter estimation technique in statistics, particularly econometrics
{Yt } t = 1,...,T, where each observation Yt is an n-dimensional multivariate random variable. We assume that the data come from a certain statistical model
Generalized_method_of_moments
the redundancy or dependency among a set of n random variables. For a given set of n random variables { X 1 , X 2 , … , X n } {\displaystyle \{X_{1}
Total_correlation
Branch of statistics
or multivariate. A univariate distribution gives the probabilities of a single random variable taking on various alternative values; a multivariate distribution
Mathematical_statistics
Probability distribution
the random variable defined, for a given constant μ, by ( Z + μ ) ν V . {\displaystyle (Z+\mu ){\sqrt {\frac {\nu }{V}}}.} This random variable has a
Student's_t-distribution
Probability distribution
family of continuous multivariate probability distributions parameterized by a vector α of positive reals. It is a multivariate generalization of the
Dirichlet_distribution
Statistical distribution of complex random variables
The standard complex normal random variable or standard complex Gaussian random variable is a complex random variable Z {\displaystyle Z} whose real
Complex_normal_distribution
Aspect of probability theory
calculation of the sum of normally distributed random variables is an instance of the arithmetic of random variables. This is not to be confused with the sum
Sum of normally distributed random variables
Sum_of_normally_distributed_random_variables
Concept in probability theory
theory, it is possible to approximate the moments of a function f of a random variable X using Taylor expansions, provided that f is sufficiently differentiable
Taylor expansions for the moments of functions of random variables
Taylor_expansions_for_the_moments_of_functions_of_random_variables
Type of signal in signal processing
serially uncorrelated random variables with a mean of zero and a finite variance; a single realization of white noise is a random shock. In some contexts
White_noise
Measure of dependence
measure that quantifies the extent to which the information in a multivariate random variable is dominated by synergistic interactions (in which case Ω ( X
Dual_total_correlation
Probability distribution
generalization of the multivariate normal distribution to matrix-valued random variables. The probability density function for the random matrix X (n × p)
Matrix_normal_distribution
Generalization of gamma distribution to multiple dimensions
distributions defined over symmetric, positive-definite random matrices (i.e. matrix-valued random variables). These distributions are of great importance in
Wishart_distribution
Probability distribution of only one random variable
random variable. This is in contrast to a multivariate distribution, the probability distribution of a random vector (consisting of multiple random variables)
Univariate_distribution
experiments, completely randomized designs are for studying the effects of one primary factor without the need to take other nuisance variables into account. This
Completely_randomized_design
Statistical model
collection of random variables indexed by time or space), such that every finite collection of those random variables has a multivariate normal distribution
Gaussian_process
Concept in statistics
statistics, a Gaussian random field (GRF) is a random field involving Gaussian probability density functions of the variables. A one-dimensional GRF is
Gaussian_random_field
Type of research design
and multivariate assumptions apply. The univariate assumptions are: Normality—For each level of the within-subjects factor, the dependent variable must
Repeated_measures_design
Fundamental theorem in probability theory and statistics
{\displaystyle {\bar {X}}_{n}} denote the sample mean (which is itself a random variable). Then the limit as n → ∞ {\displaystyle n\to \infty } of the distribution
Central_limit_theorem
How many standard deviations apart from the mean an observed datum is
data is often of considerable interest and importance… When the variables in a multivariate data set are on different scales, it makes more sense to calculate
Standard_score
Bias in causal inference
regression analysis. Multivariate analyses reveal much less information about the strength or polarity of the confounding variable than do stratification
Confounding
Probability distribution
value (α) of log 4 5 ≈ 1.16 exhibit the Pareto principle. If X is a random variable with a Pareto (Type I) distribution, then the probability that X is
Pareto_distribution
Measure of linear correlation
of the strength of the joint association between different pairs of random variables that do not necessarily have the same units. As with covariance itself
Pearson correlation coefficient
Pearson_correlation_coefficient
Expected value of a random variable given that certain conditions are known to occur
mean of a random variable is its expected value evaluated with respect to the conditional probability distribution. If the random variable can take on
Conditional_expectation
Power series derived from a discrete probability distribution
discrete random variable is a power series representation (the generating function) of the probability mass function of the random variable. Probability
Probability generating function
Probability_generating_function
Bound on probability of a random variable being far from its mean
of deviation of a random variable (with finite variance) from its mean. More specifically, the probability that a random variable deviates from its mean
Chebyshev's_inequality
Set of statistical processes for estimating the relationships among variables
model. Nonlinear models for binary dependent variables include the probit and logit model. The multivariate probit model is a standard method of estimating
Regression_analysis
Graphical tool in probability
dependent random variables". Annals of Statistics. 30 (4): 1031–1068. CiteSeerX 10.1.1.26.8965. doi:10.1214/aos/1031689016. Joe, H. (1997). Multivariate Models
Vine_copula
Overview of and topical guide to statistics
function List of probability distributions Random variable Central moment L-moment Algebra of random variables Probability Conditional probability Law of
Outline_of_statistics
Moment of a random variable minus its mean
both univariate and multivariate distributions. The n-th moment about the mean (or n-th central moment) of a real-valued random variable X is the quantity
Central_moment
Martingale difference sequence / (F:R) Maximum likelihood / (FL:R) Multivariate random variable / (F:R) Optional stopping theorem / (FS:R) Pairwise independence /
Catalog of articles in probability theory
Catalog_of_articles_in_probability_theory
Family of multivariate continuous probability distributions
the normal-inverse-gamma distribution that is defined over multivariate random variables. f ( x , σ 2 ∣ μ , λ , α , β ) = λ σ 2 π β α Γ ( α ) ( 1 σ 2
Normal-inverse-gamma distribution
Normal-inverse-gamma_distribution
General linear model that blends ANOVA and regression
accounts for very little variance in the dependent variable might actually reduce power. MANCOVA (Multivariate analysis of covariance) Keppel, G. (1991). Design
Analysis_of_covariance
Theorem of probability theory
formula for the covariance of one random variable with the value of a function of another, when the two random variables are jointly normally distributed
Stein's_lemma
Method of data analysis
if two directions through the data (or two of the original variables) are chosen at random, the clusters may be much less spread apart from each other
Principal_component_analysis
Probability distribution
of random variables limited to intervals of finite length in a wide variety of disciplines. The beta distribution is a suitable model for the random behavior
Beta_distribution
Selection of data points in statistics
Implementation usually follows a simple random sample. In addition to allowing for stratification on an ancillary variable, poststratification can be used to
Sampling_(statistics)
generalization to the multivariable case is: Theorem—Given any multivariate random variable g ^ : Ω → R m {\displaystyle {\hat {g}}:\Omega \to \mathbb {R}
Chapman–Robbins_bound
Variable capable of taking on a limited number of possible values
values of a categorical variable is referred to as a level. The probability distribution associated with a random categorical variable is called a categorical
Categorical_variable
MULTIVARIATE RANDOM-VARIABLE
MULTIVARIATE RANDOM-VARIABLE
Surname or Lastname
English (chiefly East Anglia)
English (chiefly East Anglia) : patronymic from the Middle English personal name Rand(e) (see Rand 1).
Male
Hungarian
 Variant spelling of Hungarian András, ANDOR means "man; warrior." Compare with another form of Andor.
Surname or Lastname
English
English : patronymic from Rand 1.
Female
English
Variant spelling of English Randy, RANDI means "worthy of admiration."
Surname or Lastname
English
English : variant of Brandon.
Female
English
Pet form of English Miranda, RANDY means "worthy of admiration."Â Compare with masculine Randy.Â
Surname or Lastname
English
English : variant spelling of Randall.Americanized spelling of Randel.
Boy/Male
English American
Son of Rand.
Surname or Lastname
English
English : variant of Rand 1, from the Old French oblique case.
Surname or Lastname
English
English : probably a variant of Crandon, a habitational name from Crandon in Somerset or Crandean in Falmer, Sussex. Compare Grandin.
Surname or Lastname
English or Scottish
English or Scottish : unexplained. Possibly, as Black suggests, a reduced form of Langdon.French : from the old Germanic personal name element Lando (see Land), via the oblique case, Landonis.
Male
English
Pet form of English Randall and Randolph, both RANDY means "shield-wolf." Compare with feminine Randy.
Male
English
Medieval form of English Randolf, RANDAL means "shield-wolf."
Surname or Lastname
English
English : unexplained; perhaps a variant of Francom.
Boy/Male
English
Son of Rand.
Female
English
Short form of English Miranda, RANDA means "worthy of admiration."Â
Male
Norwegian
 Norwegian form of Old Norse Arnþórr, ANDOR means "eagle of Thor." Compare with another form of Andor.
Male
English
 Variant spelling of Middle English Randulf, RANDOLF means "shield-wolf." Compare with other forms of Randolf.
Surname or Lastname
English
English : variant of Ransom.
Male
Scandinavian
 Scandinavian form of Old Norse Randolfr, RANDOLF means "shield-wolf." Compare with another form of Randolf.
MULTIVARIATE RANDOM-VARIABLE
MULTIVARIATE RANDOM-VARIABLE
Boy/Male
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Kind
Surname or Lastname
English
English : from the Middle English personal name Rawlin, Old French Raulin, a double diminutive of Raw 1, with the Anglo-Norman French suffixes -el and -in.
Male
Scottish
Variant spelling of Scottish Ruairidh, RUARAIDH means "red king."
Biblical
foolishness
Boy/Male
Hindu, Indian
Shining; Illuminating
Boy/Male
Muslim
Name of swahabi
Girl/Female
Hindu
Light of victory
Boy/Male
Hindu
Beautiful morning, Star, Following desire
Girl/Female
Indian
Beloved, Another name of Lord Vishnu, Goddess Lakshmi and a name given to karmic Yoga
Boy/Male
Indian
Karna, The great warrior, One who is born from fire (Son of the fire)
MULTIVARIATE RANDOM-VARIABLE
MULTIVARIATE RANDOM-VARIABLE
MULTIVARIATE RANDOM-VARIABLE
MULTIVARIATE RANDOM-VARIABLE
MULTIVARIATE RANDOM-VARIABLE
adv.
In a random manner.
n.
Distance to which a missile is cast; range; reach; as, the random of a rifle ball.
adv.
At random; hit or miss. (Obs.)
n.
The release of a captive, or of captured property, by payment of a consideration; redemption; as, prisoners hopeless of ransom.
n.
To redeem from captivity, servitude, punishment, or forfeit, by paying a price; to buy out of servitude or penalty; to rescue; to deliver; as, to ransom prisoners from an enemy.
p. pr. & vb. n.
of Ransom
n.
Ransom.
n.
A roving motion; course without definite direction; want of direction, rule, or method; hazard; chance; -- commonly used in the phrase at random, that is, without a settled point of direction; at hazard.
n.
Anything driven at random.
n.
Random.
v. i.
To wander at random; to scatter.
imp. & p. p.
of Ransom
n.
Extra hazard; chance; accident; random.
a.
Cruising at random on the ocean.
v. i.
To extend or grow at random.
n.
To exact a ransom for, or a payment on.
n.
Ransom; release.
v. i.
To go or stray at random.
a.
Going at random or by chance; done or made at hazard, or without settled direction, aim, or purpose; hazarded without previous calculation; left to chance; haphazard; as, a random guess.