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Τι (ποιος) είναι multivariate$97082$ - ορισμός

SIMULTANEOUS OBSERVATION AND ANALYSIS OF MORE THAN ONE OUTCOME VARIABLE

Multivariable analysis; Multivariate analysis; Multivariate Analysis; Multivariate analyses; Multivariate data analysis; Statistics/Multivariate; Multivariate methods; Multivariate data; Multivariate datasets

Multivariate normal distribution

$Left: Classification of seven multivariate normal classes. Coloured ellipses are 1 sd error ellipses. Black marks the boundaries between the classification regions. <math>p_e</math> is the probability of total classification error. Right: the error matrix. <math>p_{ij}</math> is the probability of classifying a sample from normal <math>i</math> as <math>j</math>. These are computed by the numerical method of ray-tracing <ref name="Das" /> ([https://www.mathworks.com/matlabcentral/fileexchange/84973-integrate-and-classify-normal-distributions Matlab code]).$
$Top: the probability of a bivariate normal in the domain <math>x\sin y-y\cos x>1</math> (blue regions). Middle: the probability of a trivariate normal in a toroidal domain. Bottom: converging Monte-Carlo integral of the probability of a 4-variate normal in the 4d regular polyhedral domain defined by <math>\sum_{i=1}^4 \vert x_i \vert < 1</math>. These are all computed by the numerical method of ray-tracing. <ref name="Das"></ref>$
$'''a:''' Probability density of a function <math>\cos x^2</math> of a single normal variable <math>x</math> with <math>\mu=-2</math> and <math>\sigma=3</math>. '''b:''' Probability density of a function <math>x^y</math> of a normal vector <math>(x, y)</math>, with mean <math>\boldsymbol{\mu}=(1, 2)</math>, and covariance <math>\mathbf{\Sigma} = \begin{bmatrix} .01 & .016 \\ .016 & .04 \end{bmatrix}</math>. '''c:''' Heat map of the joint probability density of two functions of a normal vector <math>(x, y)</math>, with mean <math>\boldsymbol{\mu}=(-2, 5)</math>, and covariance <math>\mathbf{\Sigma} = \begin{bmatrix} 10 & -7 \\ -7 & 10 \end{bmatrix}</math>. '''d:''' Probability density of a function <math>\sum_{i=1}^4 \vert x_i \vert</math> of 4 iid standard normal variables. These are computed by the numerical method of ray-tracing. <ref name="Das" />$

GENERALIZATION OF THE ONE-DIMENSIONAL NORMAL DISTRIBUTION TO HIGHER DIMENSIONS

Multivariate gaussian distribution; Multivariate Gaussian distribution; Multivariate normal; Multivariate Gaussian; Bivariate Gaussian distribution; MVN; Bivariate normal distribution; Joint normality; Jointly normal; Jointly Gaussian; Jointly gaussian; Multivariate Gaussian random variable; Multinormal distribution; Jointly normally distributed; Bivariate normal; Gaussian discriminant analysis; Normal random vector; Multinormal; Multivariate normal random variable; Mardia's test; BHEP test; Gaussian random vector; Joint normal distribution; Multidimensional normal distribution; Friedman Rafsky Test; Multivariate Gaussian vector

\, \exp ( -\frac{1}{2}(\mathbf{x} - \boldsymbol\mu)^} \boldsymbol\Sigma^{-1}(\mathbf{x} - \boldsymbol\mu) ),exists only when Σ is positive-definite

https://en.wikipedia.org/wiki/Multivariate_normal_distribution

Multivariate statistics

Multivariate statistics is a subdivision of statistics encompassing the simultaneous observation and analysis of more than one outcome variable.

https://en.wikipedia.org/wiki/Multivariate_statistics

multivariate

WIKIMEDIA DISAMBIGUATION PAGE

Multivariate (disambiguation); Trivariate

[?m?lt?'v?:r??t]

¦ adjective Statistics involving two or more variable quantities.

Βικιπαίδεια

Multivariate statistics

Multivariate statistics is a subdivision of statistics encompassing the simultaneous observation and analysis of more than one outcome variable, i.e., multivariate random variables. Multivariate statistics concerns understanding the different aims and background of each of the different forms of multivariate analysis, and how they relate to each other. The practical application of multivariate statistics to a particular problem may involve several types of univariate and multivariate analyses in order to understand the relationships between variables and their relevance to the problem being studied.

In addition, multivariate statistics is concerned with multivariate probability distributions, in terms of both

how these can be used to represent the distributions of observed data;
how they can be used as part of statistical inference, particularly where several different quantities are of interest to the same analysis.

Certain types of problems involving multivariate data, for example simple linear regression and multiple regression, are not usually considered to be special cases of multivariate statistics because the analysis is dealt with by considering the (univariate) conditional distribution of a single outcome variable given the other variables.

https://en.wikipedia.org/wiki/Multivariate statistics