Copyright © Philip M. Parker, INSEAD. Terms of Use.

Covariance

Definition: Covariance

Covariance

Noun

1. Statistical measure of the variance of two random variables measured in the same mean time period.

Source: WordNet 1.7.1 Copyright © 2001 by Princeton University. All rights reserved.
 


Specialty Definition: Covariance

DomainDefinition

Mathematics

The first product moment of two variates about their mean values. Source: European Union. (references)

Mining

A statistical measure of the correlation between two variables. In geostatistics, covariance is usually treated as the simple inverse of the variogram, computed as the overall sample variance minus the variogram value. These covariance values, rather than variogram values, are actuallyused in kriging matrix equations for greater computational efficiency. (references)

Source: compiled by the editor from various references; see credits.

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Specialty Definition: Covariance

(From Wikipedia, the free Encyclopedia)

In probability theory and statistics, the covariance between two real-valued random variables X and Y, with expected values E(X) = μ and E(Y) = ν is defined as:

This is equivalent to the following formula which is commonly used in actual calculations:

For column-vector valued random variables X and Y with respective expected values μ and ν, and n and m scalar components respectively, the covariance is defined to be the n×m matrix

If X and Y are independent, then their covariance is zero. This follows because under independence, E(X·Y) = E(X)·E(Y). The converse, however, is not true: it is possible that X and Y are not independent, yet their covariance is zero.

If X and Y are real-valued random variables and c is a constant ("constant", in this context, means non-random), then the following facts are a consequence of the definition of covariance:

For vector-valued random variables, cov(X, Y) and cov(Y, X) are each other's transposes.

The covariance is sometimes called a measure of "linear dependence" between the two random variables. That phrase does not mean the same thing that it means in a more formal linear algebraic setting (see linear dependence), although that meaning is not unrelated. The correlation is a closely related concept used to measure the degree of linear dependence between two variables.

Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Covariance."

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Crosswords: Covariance

Specialty definitions using "covariance": Bingham's distribution, bivariate Laplace-Gauss distribution, bivariate normal distributionCOVARIANCE MATRIXdispersion stabilising transformationsequential T2 testWald-Wolfowitz test, Wiener-Khintchine theorem. (references)

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Commercial Usage: Covariance

DomainTitle

Books

  • Analysis of Covariance (reference)

  • Analysis of Messy Data, Volume III: Analysis of Covariance (reference)

  • Covariance Analysis for Seismic Signal Processing (Geophysical Development Series, V. 8.) (reference)

  • Formal Structure of Electromagnetics: General Covariance and Electromagnetics (Series in Physics.) (reference)

  • Multiple Regression and the Analysis of Variance and Covariance (reference)

    (more book examples)

Source: compiled by the editor from various references; see credits.

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Usage Frequency: Covariance

"Covariance" is generally used as a noun (singular) -- approximately 100.00% of the time. "Covariance" is used about 49 times out of a sample of 100 million words spoken or written in English. Its rank is based on over 700,000 words used in the English language. Some parts-of-speech are not covered due to the samples used by the British National Corpus. (note: percents less than one-hundredth of one percent have been omitted)
Parts of SpeechPercentUsage per
100 Million Words
Rank in English
Noun (singular)100%4948,677

Source: compiled by the editor from several corpora; see credits.

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Expression: Covariance

Hypenated Usage

Ending with "covariance": variance-covariance.

Source: compiled by the editor from various references; see credits.

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Frequency of Internet Keywords: Covariance

The following statistics estimate the number of searches per day across the major English-language search engines as identified by various trade publications. Hyperlinks lead to commercial use of the expression at Amazon.com.
 
ExpressionFrequency
per Day

covariance

44

covariance matrix

10

covariance definition

4

correlation covariance

3

covariance eddy

3

covariance matrix variance

3

covariance formula

2

covariance statistics

2
Source: compiled by the editor from various references; see credits.

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Modern Translation: Covariance

Language Translations for "covariance"; alternative meanings/domain in parentheses.

Danish

  

kovarians (covariate). (various references)

   

Dutch

  

covariantie. (various references)

   

Finnish

  

kovarianssi. (various references)

   

French

  

covariance empirique (empiric covariance), covariance (empiric covariance). (various references)

   

German

  

Kovarianz. (various references)

   

Greek 

  

συνδιασπορά. (various references)

   

Italian

  

covarianza. (various references)

   

Korean 

  

공분산. (various references)

   

Pig Latin

  

ovariancecay

   

Portuguese

  

covariância. (various references)

   

Russian 

  

ковариационный анализ (analysis of covariance). (various references)

   

Spanish

  

covarianza. (various references)

   

Swedish

  

kovarians. (various references)

Source: compiled by the editor from various translation references.

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Derivations & Misspellings: Covariance

Derivations

Words beginning with "covariance": covariances. (additional references)


Misspellings

"Covariance" is suggested in spellcheckers for the following: cuverian. (additional references)

Source: compiled by the editor, based on several corpora (additional references).

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Anagrams: Covariance

Scrabble® Enable2K-Verified Anagrams

Words within the letters "a-a-c-c-e-i-n-o-r-v"

-2 letters: cavicorn, cocinera, variance, veronica.

-3 letters: acarine, acronic, avarice, carinae, carioca, caviare, cocaine, concave, cornice, corvina, corvine, crocein, crocine, ocarina, oceanic, ovarian, vaccina, vaccine.

-4 letters: acinar, aeonic, arcane, arnica, cancer, carina, carnie, carven, cavern, caviar, cicero, cocain, coiner, cornea, crania, craven, naiver, novice, orcein, ravine, recoin, renvoi, vainer, voicer.

-5 letters: acari, acorn, aecia, aiver, anear.

 Words containing the letters "a-a-c-c-e-i-n-o-r-v"
 

+1 letter: covariances.

 

+2 letters: clairvoyance, coacervation.

 

+3 letters: clairvoyances, coacervations, revaccination.

 

+4 letters: revaccinations.

Source: compiled by the editor from various references; see credits.

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INDEX

1. Definition
2. Crosswords
3. Usage: Commercial
4. Usage Frequency
5. Expressions
6. Expressions: Internet
7. Translations: Modern
8. Derivations
9. Anagrams
10. Bibliography


  

Copyright © Philip M. Parker, INSEAD. Terms of Use.