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Multivariable generalization of the Student's t-distribution
In statistics, the multivariate t-distribution (or multivariate Student distribution) is a multivariate probability distribution. It is a generalization
Multivariate_t-distribution
Generalization of the one-dimensional normal distribution to higher dimensions
theory and statistics, the multivariate normal distribution, multivariate Gaussian distribution, or joint normal distribution is a generalization of the
Multivariate normal distribution
Multivariate_normal_distribution
Probability distribution
of probability, multivariate Laplace distributions are extensions of the Laplace distribution and the asymmetric Laplace distribution to multiple variables
Multivariate Laplace distribution
Multivariate_Laplace_distribution
Concept in probability theory
The multivariate stable distribution is a multivariate probability distribution that is a multivariate generalisation of the univariate stable distribution
Multivariate stable distribution
Multivariate_stable_distribution
Type of probability distribution
probability space, the multivariate or joint probability distribution for X , Y , … {\displaystyle X,Y,\ldots } is a probability distribution that gives the probability
Joint probability distribution
Joint_probability_distribution
Type of probability distribution
T-squared distribution (T2), proposed by Harold Hotelling, is a multivariate probability distribution that is tightly related to the F-distribution and
Hotelling's T-squared distribution
Hotelling's_T-squared_distribution
Concept in statistics
matrix t-distribution (or matrix variate t-distribution) is the generalization of the multivariate t-distribution from vectors to matrices. The matrix t-distribution
Matrix_t-distribution
Simultaneous observation and analysis of more than one outcome variable
conditional distribution of a single outcome variable given the other variables. Multivariate analysis (MVA) is based on the principles of multivariate statistics
Multivariate_statistics
Topics referred to by the same term
phrase "T distribution" may refer to Student's t-distribution in univariate probability theory, Hotelling's T-square distribution in multivariate statistics
T_distribution
Family of distributions that generalize the multivariate normal distribution
elliptical distribution is any member of a broad family of probability distributions that generalize the multivariate normal distribution. In the simplified
Elliptical_distribution
Probability distribution
continuous multivariate probability distributions parameterized by a vector α of positive reals. It is a multivariate generalization of the beta distribution, hence
Dirichlet_distribution
Multivariate parameter family of continuous probability distributions
normal-inverse-Wishart distribution (or Gaussian-inverse-Wishart distribution) is a multivariate four-parameter family of continuous probability distributions. It is
Normal-inverse-Wishart distribution
Normal-inverse-Wishart_distribution
Generalization of gamma distribution to multiple dimensions
Bayesian statistics, the Wishart distribution is the conjugate prior of the inverse covariance-matrix of a multivariate-normal random vector. Suppose G
Wishart_distribution
Concept in probability theory
and t n {\displaystyle t_{n}} refer to the normal distribution and Student's t-distribution, respectively, or to the multivariate normal distribution and
Conjugate_prior
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
Procedure for comparing multivariate sample means
dependent variables whose linear combination follows a multivariate normal distribution, multivariate variance-covariance matrix homogeneity, and linear relationship
Multivariate analysis of variance
Multivariate_analysis_of_variance
Family of multivariate continuous probability distributions
normal-inverse-gamma distribution (or Gaussian-inverse-gamma distribution) is a four-parameter family of multivariate continuous probability distributions. It is the
Normal-inverse-gamma distribution
Normal-inverse-gamma_distribution
Probability distribution used in multivariate hypothesis testing
In statistics, Wilks' lambda distribution (named for Samuel S. Wilks), is a probability distribution used in multivariate hypothesis testing, especially
Wilks's_lambda_distribution
Probability distribution
distributions Hotelling's T² distribution Multivariate Student distribution Standard normal table (Z-distribution table) t statistic Tau distribution
Student's_t-distribution
the binomial distribution. The multivariate normal distribution, a generalization of the normal distribution. The multivariate t-distribution, a generalization
List of probability distributions
List_of_probability_distributions
theory and statistics, the generalized multivariate log-gamma (G-MVLG) distribution is a multivariate distribution introduced by Demirhan and Hamurkaroglu
Generalized multivariate log-gamma distribution
Generalized_multivariate_log-gamma_distribution
Probability distribution
(1986), which applies to multivariate cases beyond normality, e.g. skew multivariate t distribution and others. The distribution is a particular case of
Skew_normal_distribution
Probability distribution
covariance matrix of a multivariate normal distribution. We say X {\displaystyle \mathbf {X} } follows an inverse Wishart distribution, denoted as X ∼ W −
Inverse-Wishart_distribution
Multivariate probability distribution
normal-Wishart distribution (or Gaussian-Wishart distribution) is a multivariate four-parameter family of continuous probability distributions. It is the
Normal-Wishart_distribution
Probability distribution
normal distribution or matrix Gaussian distribution is a probability distribution that is a generalization of the multivariate normal distribution to matrix-valued
Matrix_normal_distribution
Probability distribution
probability theory and statistics, the Rayleigh distribution is a continuous probability distribution for nonnegative-valued random variables. Up to rescaling
Rayleigh_distribution
Continuous probability distribution
theory and statistics, the logistic distribution is a continuous probability distribution. Its cumulative distribution function is the logistic function
Logistic_distribution
Probability distribution
distribution is the Student t-distribution with one degree of freedom, the multidimensional Cauchy density is the multivariate Student distribution with
Cauchy_distribution
Probability distribution on complex matrices
N R (1963). "Statistical analysis based on a certain multivariate complex Gaussian distribution (an introduction)". Ann. Math. Statist. 34: 152–177. doi:10
Complex_Wishart_distribution
Probability distribution
logistic distributions). (For other names, see Naming.) The univariate probability distribution is generalized for vectors in the multivariate normal distribution
Normal_distribution
Statistical linear model
measurements, and follow a multivariate normal distribution. If the errors do not follow a multivariate normal distribution, generalized linear models
General_linear_model
Taxonomy of statistical data elements
Examples of distributions used to describe correlated random vectors are the multivariate normal distribution and multivariate t-distribution. In general
Statistical_data_type
Probability distribution
noncentral t-distribution generalizes Student's t-distribution using a noncentrality parameter. Whereas the central probability distribution describes
Noncentral_t-distribution
Statistical distribution for dependence between random variables
and statistics, a copula is a multivariate cumulative distribution function for which the marginal probability distribution of each variable is uniform
Copula_(statistics)
Statistical relationship
from a multivariate normal distribution. Similarly for two stochastic processes { X t } t ∈ T {\displaystyle \left\{X_{t}\right\}_{t\in {\mathcal {T}}}}
Correlation
same color is easier to calculate. See the formula below under multivariate distribution. No exact formula for the mean is known (short of complete enumeration
Wallenius' noncentral hypergeometric distribution
Wallenius'_noncentral_hypergeometric_distribution
Discrete probability distribution
"with-replacement" distribution and the multivariate hypergeometric is the "without-replacement" distribution. The properties of this distribution are given in
Hypergeometric_distribution
Fourier transform of the probability density function
London: Griffin. Kotz, Samuel; Nadarajah, Saralees (2004). Multivariate T Distributions and Their Applications. Cambridge University Press. Manolakis
Characteristic function (probability theory)
Characteristic_function_(probability_theory)
Multivariate continuous probability distribution
of multivariate normal distributions, and related distributions. The probability density function of the matrix F {\displaystyle F} distribution is:
Matrix_F-distribution
Mathematical function for the probability a given outcome occurs in an experiment
probability distributions include the binomial distribution, the hypergeometric distribution, and the normal distribution. A commonly encountered multivariate distribution
Probability_distribution
N R (1963). "Statistical Analysis Based on a Certain Multivariate Complex Gaussian Distribution: an Introduction". Ann. Math. Statist. 34 (1): 152–177
Complex inverse Wishart distribution
Complex_inverse_Wishart_distribution
statistics, the multivariate Behrens–Fisher problem is the problem of testing for the equality of means from two multivariate normal distributions when the covariance
Multivariate Behrens–Fisher problem
Multivariate_Behrens–Fisher_problem
Probability distribution
log-t distribution also has applications in hydrology and in analyzing data on cancer remission. Analogous to the log-normal distribution, multivariate forms
Log-t_distribution
Involving a single variable
treated using certain types of multivariate statistical analyses and may be represented using multivariate distributions. In addition to the question of
Univariate
Probability that random variable X is less than or equal to x
functions are also used to specify the distribution of multivariate random variables. The cumulative distribution function of a real-valued random variable
Cumulative distribution function
Cumulative_distribution_function
Statistical hypothesis test
Student's t-distribution under the null hypothesis. It is most commonly applied when the test statistic would follow a normal distribution if the value
Student's_t-test
Family of continuous probability distributions
statistics, the skewed generalized "t" distribution is a family of continuous probability distributions. The distribution was first introduced by Panayiotis
Skewed generalized t distribution
Skewed_generalized_t_distribution
Statistical distance measure
later obtained the sampling distribution of Mahalanobis distance, under the assumption of equal dispersion. It is a multivariate generalization of the absolute
Mahalanobis_distance
Statistical test for dose-response trends
Instead, the corresponding p-value must be adjusted, either via a multivariate t-distribution or through permutation methods. It is often cited as a precursor
Tukey's_trend_test
Generalization of gamma distribution
the Wishart distribution, and is used similarly, e.g. as the conjugate prior of the precision matrix of a multivariate normal distribution and matrix normal
Matrix_gamma_distribution
American statistician and engineer (1930–2010)
ISBN 1-58488-403-7. OCLC 56453946. Kotz, Samuel; Nadarajah, Saralees (2004). Multivariate t distributions and their applications. Cambridge: Cambridge University Press
Samuel_Kotz
Multivariate statistics Multivariate Student distribution – redirects to Multivariate t-distribution Multivariate t-distribution n = 1 fallacy N of 1 trial
List_of_statistics_articles
Class of statistical tests
testing univariate or multivariate normality and are statistically consistent against general alternatives. The normal distribution has the highest entropy
Normality_test
Statistical distribution of complex random variables
normal ratio distribution Directional statistics § Distribution of the mean (polar form) Normal distribution Multivariate normal distribution (a complex
Complex_normal_distribution
Statistical test comparing two probability distributions
Fn(x) will entirely contain F(x) with probability 1 − α. A distribution-free multivariate Kolmogorov–Smirnov goodness of fit test has been proposed by
Kolmogorov–Smirnov_test
Measure of variation in statistics
axes of the 1 sd error ellipsoid of the multivariate normal distribution. See Multivariate normal distribution: geometric interpretation. The standard
Standard_deviation
Discrete probability distribution
Poisson distribution as PoissonDistribution[ λ {\displaystyle \lambda } ], bivariate Poisson distribution as MultivariatePoissonDistribution[ θ 12 , {\displaystyle
Poisson_distribution
Probability distribution
t\sigma ,t\sigma ;c\\p+q+t\sigma ;\end{bmatrix}}.} A multivariate generalized beta pdf extends the univariate distributions listed above
Generalized_beta_distribution
British–Iranian economist
volatilities and conditional correlations in futures markets with a multivariate T distribution. CESifo. Retrieved 11 February 2010. Mohammad Hashem Pesaran;
M._Hashem_Pesaran
Probability distribution
}})} is a multivariate normal distribution, then Y i = exp ( X i ) {\displaystyle Y_{i}=\exp(X_{i})} has a multivariate log-normal distribution. The exponential
Log-normal_distribution
Probability distribution
univariate Pareto distribution has been extended to a multivariate Pareto distribution. The likelihood function for the Pareto distribution parameters α and
Pareto_distribution
Fourth standardized moment in statistics
that the joint cumulants of degree greater than two for any multivariate normal distribution are zero. For two random variables, X and Y, not necessarily
Kurtosis
Middle quantile of a data set or probability distribution
symmetrized distribution and which is close to the population median. The Hodges–Lehmann estimator has been generalized to multivariate distributions. The Theil–Sen
Median
Chinese mathematician and statistician (born 1940)
develop generalized multivariate analysis, which extends classical multivariate analysis beyond the multivariate normal distribution to more general elliptical
Fang_Kaitai
Statistical modeling method
estimates are maximum likelihood estimates when ε follows a multivariate normal distribution with a known covariance matrix. Let's denote each data point
Linear_regression
Statistical measure of variability
Analogously to how the median generalizes to the geometric median (GM) in multivariate data, MAD can be generalized to the median of distances to GM (MADGM)
Median_absolute_deviation
Statistical hypothesis test
samples"). The Wilcoxon test is a good alternative to the t-test when the normal distribution of the differences between paired individuals cannot be assumed
Wilcoxon_signed-rank_test
Generalization of beta distribution
Here β p ( a , b ) {\displaystyle \beta _{p}\left(a,b\right)} is the multivariate beta function: β p ( a , b ) = Γ p ( a ) Γ p ( b ) Γ p ( a + b ) {\displaystyle
Matrix variate beta distribution
Matrix_variate_beta_distribution
Probability distribution
statistics, the grouped Dirichlet distribution (GDD) is a multivariate generalization of the Dirichlet distribution It was first described by Ng et al
Grouped Dirichlet distribution
Grouped_Dirichlet_distribution
data set over time. multimodal distribution multivariate analysis multivariate kernel density estimation multivariate random variable A vector whose components
Glossary of probability and statistics
Glossary_of_probability_and_statistics
Probability distribution
2307/2683252. JSTOR 2683252. Eltoft, T.; Taesu Kim; Te-Won Lee (2006). "On the multivariate Laplace distribution" (PDF). IEEE Signal Processing Letters
Laplace_distribution
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
Statistical property
K.; Tang, J. (1984). "Distribution of likelihood ratio statistic for testing equality of covariance matrices of multivariate Gaussian models". Biometrika
Homoscedasticity and heteroscedasticity
Homoscedasticity_and_heteroscedasticity
Probability distribution
Equivalently, it is the distribution of the Euclidean distance between a multivariate Gaussian random variable and the origin. The chi distribution describes the
Chi_distribution
Fundamental theorem in probability theory and statistics
limit theorem states that when scaled, sums converge to a multivariate normal distribution. Summation of these vectors is done component-wise. For i =
Central_limit_theorem
Empirical law on the variance of species in a habitat
size (n) needed is n = ( t / D ) 2 m {\displaystyle n={\frac {(t/D)^{2}}{m}}} where t is critical level of the t distribution for the type 1 error with
Taylor's_law
Probability distribution
inverse Wishart distribution, and is used similarly, e.g. as the conjugate prior of the covariance matrix of a multivariate normal distribution or matrix normal
Inverse matrix gamma distribution
Inverse_matrix_gamma_distribution
Robust and nonparametric estimator of a population's location parameter
populations. It has been generalized from univariate populations to multivariate populations, which produce samples of vectors. It is based on the Wilcoxon
Hodges–Lehmann_estimator
Statistical estimator
concentration matrix or inverse covariance matrix) of a multivariate elliptical distribution. Through the use of an L 1 {\displaystyle L_{1}} penalty
Graphical_lasso
Statistical method
Bootstrapping is a procedure for estimating the distribution of an estimator by resampling (often with replacement) one's data or a model which is estimated
Bootstrapping_(statistics)
Probability distribution and special case of gamma distribution
showed that the chi-squared distribution arose from such a multivariate normal approximation to the multinomial distribution, taking careful account of
Chi-squared_distribution
Statistical test
meet the assumption of multivariate normality. Bartlett's test Levene's test Box, G.E.P. (1 December 1949). "A General Distribution Theory for a Class of
Box's_M_test
Nonparametric test of the null hypothesis
pp. xvi+463. ISBN 978-0-387-35212-1. MR 0395032. Oja, Hannu (2010). Multivariate nonparametric methods with R: An approach based on spatial signs and
Mann–Whitney_U_test
Statistical method for analysing climate data
elliptically distributed (e.g., is distributed as a multivariate normal distribution or a multivariate t-distribution) then the first DCA pattern (DCA1) is defined
Directional component analysis
Directional_component_analysis
Measure of the asymmetry of random variables
Mathematics, EMS Press, 2001 [1994] An Asymmetry Coefficient for Multivariate Distributions by Michel Petitjean On More Robust Estimation of Skewness and
Skewness
Random variable with multiple component dimensions
the joint probability distribution, the joint distribution, or the multivariate distribution of the random vector. The distributions of each of the component
Multivariate_random_variable
Probability distribution on a hyper-sphere of arbitrary dimension
hypersphere, see: projected normal distribution § note on density definition. Starting from a multivariate normal distribution with isotropic covariance κ −
Von_Mises–Fisher_distribution
Branch of statistics
distributions include the binomial distribution, the hypergeometric distribution, and the normal distribution. The multivariate normal distribution is
Mathematical_statistics
Particular case of the generalized extreme value distribution
related to the generalized multivariate log-gamma distribution provides a multivariate version of the Gumbel distribution. Gumbel has shown that the maximum
Gumbel_distribution
Statistical model
those random variables has a multivariate normal distribution. The distribution of a Gaussian process is the joint distribution of all those (infinitely many)
Gaussian_process
Measure of covariance of components of a random vector
characteristic mutation operator draws the update step from a multivariate normal distribution using an evolving covariance matrix. There is a formal proof
Covariance_matrix
Probability distribution
distribution. The multivariate Logistic-beta distribution along with coordinate-wise logistic transformation can be considered as a multivariate generalization
Beta_distribution
calculate bivariate normal distribution probabilities and, from there, in the calculation of multivariate normal distribution probabilities. It also frequently
Owen's_T_function
Probability distribution of only one random variable
a univariate distribution is a probability distribution of only one random variable. This is in contrast to a multivariate distribution, the probability
Univariate_distribution
Function of the observed sample results
PMC 2816758. PMID 19921345. Brereton, Richard G. (2021). "P values and multivariate distributions: Non-orthogonal terms in regression models". Chemometrics and
P-value
inverted Dirichlet distribution is a multivariate generalization of the beta prime distribution, and is related to the Dirichlet distribution. It was first
Inverted Dirichlet distribution
Inverted_Dirichlet_distribution
Statistical model for a binary dependent variable
not true, however, because logistic regression does not require the multivariate normal assumption of discriminant analysis. The assumption of linear
Logistic_regression
Table that displays the frequency of variables
is a type of table in a matrix format that displays the multivariate frequency distribution of the variables. They are heavily used in survey research
Contingency_table
Variable representing a random phenomenon
Aleatoricism Algebra of random variables Event (probability theory) Multivariate random variable Pairwise independent random variables Observable variable
Random_variable
Concept in Bayesian statistics
posterior probability distributions or predictive probability distributions. Their generalization to disconnected or multivariate sets is called credible
Credible_interval
MULTIVARIATE T-DISTRIBUTION
MULTIVARIATE T-DISTRIBUTION
MULTIVARIATE T-DISTRIBUTION
MULTIVARIATE T-DISTRIBUTION
MULTIVARIATE T-DISTRIBUTION
MULTIVARIATE T-DISTRIBUTION
MULTIVARIATE T-DISTRIBUTION
MULTIVARIATE T-DISTRIBUTION
MULTIVARIATE T-DISTRIBUTION