covariance

English

Etymology

co- +‎ variance

Pronunciation

• (UK) IPA^(key): /kəʊˈvɛː.ɹi.əns/
• (US, Mary–marry–merry distinction) IPA^(key): /koʊˈvæɹ.i.əns/
• (US, Mary–marry–merry merger) IPA^(key): /ˈkoʊˈvɛɹ.i.əns/

  • Audio (Connecticut)

    (file)

• (General Australian) IPA^(key): /kəʉˈveː.ɹi.əns/

Noun

covariance (plural covariances)

1. (statistics) A statistical measure defined as $\scriptstyle \operatorname {Cov} (X,Y)=\operatorname {E} ((X-\mu )(Y-\nu ))$ given two real-valued random variables X and Y, with expected values $\scriptstyle E(X)\,=\,\mu$ and $\scriptstyle E(Y)\,=\,\nu$.
   • 2002, Karl G. Jöreskog, Dag Sörbom, PRELIS 2 User's Reference Guide, Scientific Software International, page 28:

     The elements of such a correlation matrix do not have asymptotic variances and covariances of the form (1.2), even if S has a Wishart distribution.

   • 1997, Michael Patrick Allen, Understanding Regression Analysis, Plenum Press, page 31:

     Consequently, it can be shown that a covariance of two binary variables measures the extent to which the observed joint distribution of these variables differs from their expected joint distribution under the assumption that they are statistically independent.

   • 2005, Steven J. Janke, Frederick Tinsley, Introduction to Linear Models and Statistical Inference, Wiley, page 133:

     The covariance of X and Y is the expected value of the product of two random variables, X − E(X) and Y − E(Y). […] If two random variables tend to act like opposites, one is high when the other is low and vice versa, then the covariance will be negative. If two random variables tend to be high and low at the same time, then the covariance will be positive. In fact, the covariance measures the extent of a linear relationship between the two random variables.

2. (object-oriented programming) The conversion of data types from wider to narrower in certain situations.

   Coordinate term: contravariance

   • 2014, Benjamin J. Evans, David Flanagan, Java in a Nutshell, O'Reilly, →ISBN, page 149:

     As we will see in Chapter 8, we see both covariance and contravariance throughout the Java Collections. They largely exist to ensure that the generics just “do the right thing” and behave in a manner that should not surprise the developer.

Derived terms

• autocovariance
• covariance function
• covariance mapping
• covariance matrix
• eddy covariance
• subcovariance

 

Related terms

• covariant

Translations

statistical measure

• Basque: kobariantza
• Catalan: covariància f
• Chinese:

  Mandarin: 協方差／协方差 (zh) (xiéfāngchā), 共變異數／共变异数 (gòngbiànyìshù)

• Czech: kovariance f
• Dutch: covariantie (nl) f
• Esperanto: kunvarianco
• Finnish: kovarianssi (fi)
• French: covariance (fr) f
• German: Kovarianz f
• Indonesian: kovariansi
• Italian: covarianza (it) f
• Kazakh: ковариация (kovariasiä)
• Kyrgyz: ковариация (kovariatsiya)
• Polish: kowariancja (pl) f
• Portuguese: covariância f
• Romanian: covarianță (ro) f
• Russian: ковариа́ция (ru) f (kovariácija)
• Spanish: covariación f, covarianza f
• Sundanese: kovarian
• Tagalog: kaalig
• Turkish: kovaryans

object-oriented programming

• Chinese:

  Mandarin: 協變／协变 (zh) (xiébiàn)

• Finnish: kovarianssi (fi)
• French: covariance (fr) f
• German: Kovarianz f
• Japanese: 共変性 (きょうへんせい, kyōhensei)
• Kazakh: коварианттық (kovarianttyq), коварианттылық (kovarianttylyq)
• Russian: ковариантность (ru) f (kovariantnostʹ)

Further reading

• covariance on Wikipedia.Wikipedia
• covariance and contravariance (computer science) on Wikipedia.Wikipedia
• Covariance on Wolfram MathWorld

French

Pronunciation

• IPA^(key): /kɔ.va.ʁjɑ̃s/

• Audio

  (file)

Noun

covariance f (plural covariances)

1. (statistics) covariance
2. (object-oriented programming) covariance

Further reading

• “covariance”, in Trésor de la langue française informatisé [Digitized Treasury of the French Language], 2012.