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第647行： − + − − 多元互信息函数推广了数学 x1，x2 / math 当且仅当 math i (x1; x2)0 / math 为任意多个变量的成对独立情形。N 个变量是相互独立的当且仅当数学2 ^ n-n-1 / 数学互信息函数消失数学 i (x1; ... ; xk)0 / 数学 n ge k ge 2 / 数学(定理2)。在这个意义上，数学 i (x1; ... ; xk)0 / math 可以用作改进的统计独立性标准。 − − +
→多元统计独立性 Multivariate statistical independence
The multivariate mutual-information functions generalize the pairwise independence case that states that <math>X_1,X_2</math> if and only if <math>I(X_1;X_2)=0</math>, to arbitrary numerous variable. n variables are mutually independent if and only if the <math>2^n-n-1</math> mutual information functions vanish <math>I(X_1;...;X_k)=0</math> with <math>n \ge k \ge 2</math> (theorem 2 <ref name=e21090869/>). In this sense, the <math>I(X_1;...;X_k)=0</math> can be used as a refined statistical independence criterion.
The multivariate mutual-information functions generalize the pairwise independence case that states that <math>X_1,X_2</math> if and only if <math>I(X_1;X_2)=0</math>, to arbitrary numerous variable. n variables are mutually independent if and only if the <math>2^n-n-1</math> mutual information functions vanish <math>I(X_1;...;X_k)=0</math> with <math>n \ge k \ge 2</math> (theorem 2 <ref name=e21090869/>). In this sense, the <math>I(X_1;...;X_k)=0</math> can be used as a refined statistical independence criterion.
The multivariate mutual-information functions generalize the pairwise independence case that states that <math>X_1,X_2</math> if and only if <math>I(X_1;X_2)=0</math>, to arbitrary numerous variable. n variables are mutually independent if and only if the <math>2^n-n-1</math> mutual information functions vanish <math>I(X_1;...;X_k)=0</math> with <math>n \ge k \ge 2</math> (theorem 2 ). In this sense, the <math>I(X_1;...;X_k)=0</math> can be used as a refined statistical independence criterion.
The multivariate mutual-information functions generalize the pairwise independence case that states that 𝑋1,𝑋2 if and only if 𝐼(𝑋1;𝑋2)=0, to arbitrary numerous variable. n variables are mutually independent if and only if the 2𝑛−𝑛−1 mutual information functions vanish 𝐼(𝑋1;...;𝑋𝑘)=0 with 𝑛≥𝑘≥2 (theorem 2). In this sense, the 𝐼(𝑋1;...;𝑋𝑘)=0 can be used as a refined statistical independence criterion.
多元互信息函数将𝑋1，𝑋2当且仅当𝐼（𝑋1；𝑋2）=0的两两独立情况推广到任意多变量。当且仅当2𝑛-𝑛-1互信息函数为𝑛（𝑛1；…；𝑋𝑘）=0且𝑛≥2时，n个变量相互独立（定理2）。从这个意义上讲，𝐼（𝑋1；…；𝑋𝑘）=0可以用作一个精确的统计独立性标准。
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