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Area Digital technology – Fundamental concepts / Information theory

IEV ref171-07-23

Symbol
H( X|Y ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aacaWGibWaaeWaaeaacaWGybGaaiiFaiaadMfaaiaawIcacaGLPaaa aaa@4218@

en
conditional entropy
mean conditional information content
average conditional information content
mean value of the conditional information content of the events in a finite set of mutually exclusive and jointly exhaustive events, given the occurrence of the events in another set of mutually exclusive and jointly exhaustive events

H(X|Y)= i=1 n j=1 m p( x i , y j )I( x i | y j ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aacaWGibGaaiikaiaadIfacaGG8bGaamywaiaacMcacqGH9aqpdaae WbqaamaaqahabaGaamiCaiaacIcacaWG4bWaaSbaaSqaaiaadMgaae qaaOGaaiilaiaadMhadaWgaaWcbaGaamOAaaqabaGccaGGPaGaeyyX ICTaamysaiaacIcacaWG4bWaaSbaaSqaaiaadMgaaeqaaOGaaiiFai aadMhadaWgaaWcbaGaamOAaaqabaGccaGGPaaaleaacaWGQbGaeyyp a0tcLboacaaIXaaaleaacaWGTbaaniabggHiLdaaleaacaWGPbGaey ypa0tcLboacaaIXaaaleaacaWGUbaaniabggHiLdaaaa@625F@

where X={ x 1 ,, x n } MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aacaWGybGaeyypa0ZaaiWaaeaacaWG4bWaaSbaaSqaaKqzGdGaaGym aaWcbeaakiaacYcacaGGUaGaaiOlaiaac6cacaWG4bWaaSbaaSqaai aad6gaaeqaaaGccaGL7bGaayzFaaaaaa@494E@ is the set of events x i ( i=1,,n ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aacaWG4bWaaSbaaSqaaiaadMgaaeqaaOWaaeWaaeaacaWGPbGaeyyp a0tcLbuacaaIXaGccaGGSaGaaiOlaiaac6cacaGGUaGaamOBaaGaay jkaiaawMcaaaaa@47D2@ , Y={ y 1 ,, y m } MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aacaWGzbGaeyypa0ZaaiWaaeaacaWG5bWaaSbaaSqaaKqzGdGaaGym aaWcbeaakiaacYcacaGGUaGaaiOlaiaac6cacaWG5bWaaSbaaSqaai aad2gaaeqaaaGccaGL7bGaayzFaaaaaa@4950@ is the set of events y j ( j=1,,m ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aacaWG5bWaaSbaaSqaaiaadQgaaeqaaOWaaeWaaeaacaWGQbGaeyyp a0tcLbuacaaIXaGaaiilaOGaaiOlaiaac6cacaGGUaGaamyBaaGaay jkaiaawMcaaaaa@47D4@ , I( x i | y j ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aacaWGjbWaaeWaaeaacaWG4bWaaSbaaSqaaiaadMgaaeqaaOGaaiiF aiaadMhadaWgaaWcbaGaamOAaaqabaaakiaawIcacaGLPaaaaaa@44A2@ is the conditional information content of x i MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aacaWG4bWaaSbaaSqaaiaadMgaaeqaaaaa@3F1E@ given y j MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aacaWG5bWaaSbaaSqaaiaadQgaaeqaaaaa@3F20@ , and p( x i , y j ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aacaWGWbWaaeWaaeaacaWG4bWaaSbaaSqaaiaadMgaaeqaaOGaaiil aiaadMhadaWgaaWcbaGaamOAaaqabaaakiaawIcacaGLPaaaaaa@4479@ the joint probability that both events occur


[SOURCE: IEC 80000-13:2008, 13-32, modified – Addition of information useful for the context of the IEV, and adaptation to the IEV rules]


fr
entropie conditionnelle, f
DÉCONSEILLÉ: néguentropie conditionnelle, f
espérance mathématique de la quantité d'information conditionnelle des événements d'un ensemble exhaustif d'événements s'excluant mutuellement, lorsque se sont réalisés les événements d'un autre ensemble exhaustif d'événements s'excluant mutuellement

H(X|Y)= i=1 n j=1 m p( x i , y j )I( x i | y j ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aacaWGibGaaiikaiaadIfacaGG8bGaamywaiaacMcacqGH9aqpdaae WbqaamaaqahabaGaamiCaiaacIcacaWG4bWaaSbaaSqaaiaadMgaae qaaOGaaiilaiaadMhadaWgaaWcbaGaamOAaaqabaGccaGGPaGaeyyX ICTaamysaiaacIcacaWG4bWaaSbaaSqaaiaadMgaaeqaaOGaaiiFai aadMhadaWgaaWcbaGaamOAaaqabaGccaGGPaaaleaacaWGQbGaeyyp a0tcLboacaaIXaaaleaacaWGTbaaniabggHiLdaaleaacaWGPbGaey ypa0tcLboacaaIXaaaleaacaWGUbaaniabggHiLdaaaa@625F@

X={ x 1 ,, x n } MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aacaWGybGaeyypa0ZaaiWaaeaacaWG4bWaaSbaaSqaaKqzGdGaaGym aaWcbeaakiaacYcacaGGUaGaaiOlaiaac6cacaWG4bWaaSbaaSqaai aad6gaaeqaaaGccaGL7bGaayzFaaaaaa@494E@ est l'ensemble d'événements x i ( i=1,,n ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aacaWG4bWaaSbaaSqaaiaadMgaaeqaaOWaaeWaaeaacaWGPbGaeyyp a0tcLbuacaaIXaGccaGGSaGaaiOlaiaac6cacaGGUaGaamOBaaGaay jkaiaawMcaaaaa@47D2@ , Y={ y 1 ,, y m } MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aacaWGzbGaeyypa0ZaaiWaaeaacaWG5bWaaSbaaSqaaKqzGdGaaGym aaWcbeaakiaacYcacaGGUaGaaiOlaiaac6cacaWG5bWaaSbaaSqaai aad2gaaeqaaaGccaGL7bGaayzFaaaaaa@4950@ est l'ensemble d'événements y j ( j=1,,m ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aacaWG5bWaaSbaaSqaaiaadQgaaeqaaOWaaeWaaeaacaWGQbGaeyyp a0tcLbuacaaIXaGaaiilaOGaaiOlaiaac6cacaGGUaGaamyBaaGaay jkaiaawMcaaaaa@47D4@ , I( x i | y j ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aacaWGjbWaaeWaaeaacaWG4bWaaSbaaSqaaiaadMgaaeqaaOGaaiiF aiaadMhadaWgaaWcbaGaamOAaaqabaaakiaawIcacaGLPaaaaaa@44A2@ est la quantité d'information conditionnelle de x i MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aacaWG4bWaaSbaaSqaaiaadMgaaeqaaaaa@3F1E@ lorsque y j MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aacaWG5bWaaSbaaSqaaiaadQgaaeqaaaaa@3F20@ s'est réalisé, p( x i , y j ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aacaWGWbWaaeWaaeaacaWG4bWaaSbaaSqaaiaadMgaaeqaaOGaaiil aiaadMhadaWgaaWcbaGaamOAaaqabaaakiaawIcacaGLPaaaaaa@4479@ est la probabilité de réalisation simultanée des deux événements


[SOURCE: IEC 80000-13:2008, 13-32, modifié – Ajout d’informations utiles pour le contexte de l’IEV, et adaptation aux règles de l’IEV]


ar
الانتروبيا المشروطة
القيمة المتوسطة المشروطة لمحتوى المعلومات

de
bedingte Entropie, f

fi
ehdollinen entropia
keskimääräinen ehdollinen informaatiomäärä

ja
条件付きエントロピー

pl
entropia warunkowa, f
średnia względna zawartość informacji, f

pt
entropia condicional

zh
条件熵

Publication date: 2019-03-29
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