皮爾森相關系數、皮爾遜相關系數（Person correlation coefficient）的存在性問題

文章目錄

• Wikipedia
• 翻譯

Wikipedia

Existence

The population Pearson correlation coefficient is defined in terms of moments, and therefore exists for any bivariate probability distribution for which the population covariance is defined and the marginal population variances are defined and are non-zero. Some probability distributions such as the Cauchy distribution have undefined variance and hence ρ is not defined if X or Y follows such a distribution. In some practical applications, such as those involving data suspected to follow a heavy-tailed distribution, this is an important consideration. However, the existence of the correlation coefficient is usually not a concern; for instance, if the range of the distribution is bounded, ρ is always defined.

翻譯

皮爾遜相關系數是根據矩定義的，是以，總體協方差及邊際總體方差存在且非零的任何二進制機率分布，都存在皮爾遜相關系數。某些機率分布（如柯西分布）方差不存在，是以，如果X或Y遵循此類分布，則ρ不存在。（後邊的翻譯尚未認真校對）在一些實際應用中，例如那些涉及懷疑遵循重尾分布的資料的應用中，這是一個重要的考慮因素。然而，相關系數的存在通常不是一個問題；例如，如果分布範圍有界，則始終定義ρ。