In probability theory and statistics, a sequence or other collection of random variables is independent and identically distributed (i.i.d. ) if each random variable has the same probability distribution as the others and all are mutually independent. The abbreviation i.i.d. is particularly common in statistics (often as iid, sometimes written IID), where observations in a sample are often assumed to be (more-or-less) i.i.d. for the purposes of statistical inference.

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  • In probability theory and statistics, a sequence or other collection of random variables is independent and identically distributed (i.i.d. ) if each random variable has the same probability distribution as the others and all are mutually independent. The abbreviation i.i.d. is particularly common in statistics (often as iid, sometimes written IID), where observations in a sample are often assumed to be (more-or-less) i.i.d. for the purposes of statistical inference. The assumption (or requirement) that observations be i.i.d. tends to simplify the underlying mathematics of many statistical methods: see mathematical statistics and statistical theory. However, in practical applications of statistical modeling the assumption may or may not be realistic. The generalization of exchangeable random variables is often sufficient and more easily met. The assumption is important in the classical form of the central limit theorem, which states that the probability distribution of the sum (or average) of i.i.d. variables with finite variance approaches a normal distribution.
  • En statistique, des variables indépendantes et identiquement distribuées (iid) sont des variables aléatoires qui ont toutes la même loi de probabilité et sont mutuellement indépendantes. En inférence statistique ou en apprentissage automatique, il est très courant de supposer que le tirage des échantillons d'apprentissage sont i.i.d. C'est une condition souvent nécessaire à l'application des théorèmes les plus courants. En particulier le théorème de la limite centrale dans sa forme classique stipule que la somme de variables aléatoires tendent vers une distribution normale quand ces variable sont i.i.d.
  • Nella teoria della probabilità una sequenza di variabili casuali è indipendente ed identicamente distribuita (i.i.d. ) se ognuna ha la stessa distribuzione di probabilità delle altre variabili, e sono tutte statisticamente indipendenti. L'abbreviazione i.i.d. è particolarmente comune in statistica (spesso anche iid, a volte IID), dove le osservazioni di un campione sono presupposte (più o meno) i.i. d per l'inferenza statistica. Il presupposto (o requisito) che le osservazioni sono i.i. d tende a facilitare la matematica di molti metodi statistici. Tuttavia, nelle applicazioni pratiche questo può o non può o essere realistico. Ciò è importante nella forma classica del teorema del limite centrale, che dichiara che la distribuzione di probabilità della somma (o della media) delle variabili i.i. d con media e varianza finite si avvicina alla distribuzione normale.
  • I sannolikhetsteorin är en samling slumpvariabler oberoende och likafördelade (förkortat o.l.f. ; även i.i.d. efter engelskans independent and identically distributed), om de dels är oberoende av varandra och dels kommer från samma sannolikhetsfördelningsfunktion. Med andra ord är de stokastiska variablerna (Xi)iєI o.l.f. , om varje par av olika variabler Xi och Xj har samma sannolikhetsfördelning, och dessutom Xj har denna sannolikhetsfördelning även om man betingar på att man vet vad värdet av Xi är.
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  • IID
  • iid
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  • In probability theory and statistics, a sequence or other collection of random variables is independent and identically distributed (i.i.d. ) if each random variable has the same probability distribution as the others and all are mutually independent. The abbreviation i.i.d. is particularly common in statistics (often as iid, sometimes written IID), where observations in a sample are often assumed to be (more-or-less) i.i.d. for the purposes of statistical inference.
  • En statistique, des variables indépendantes et identiquement distribuées (iid) sont des variables aléatoires qui ont toutes la même loi de probabilité et sont mutuellement indépendantes. En inférence statistique ou en apprentissage automatique, il est très courant de supposer que le tirage des échantillons d'apprentissage sont i.i.d. C'est une condition souvent nécessaire à l'application des théorèmes les plus courants.
  • Nella teoria della probabilità una sequenza di variabili casuali è indipendente ed identicamente distribuita (i.i.d. ) se ognuna ha la stessa distribuzione di probabilità delle altre variabili, e sono tutte statisticamente indipendenti. L'abbreviazione i.i.d. è particolarmente comune in statistica (spesso anche iid, a volte IID), dove le osservazioni di un campione sono presupposte (più o meno) i.i. d per l'inferenza statistica. Il presupposto (o requisito) che le osservazioni sono i.i.
  • I sannolikhetsteorin är en samling slumpvariabler oberoende och likafördelade (förkortat o.l.f. ; även i.i.d. efter engelskans independent and identically distributed), om de dels är oberoende av varandra och dels kommer från samma sannolikhetsfördelningsfunktion. Med andra ord är de stokastiska variablerna (Xi)iєI o.l.f.
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  • Independent and identically-distributed random variables
  • Variable indépendante et identiquement distribuée
  • Variabili indipendenti e identicamente distribuite
  • Oberoende och likafördelade
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