• Media type: E-Article
  • Title: A Note on Correlation Curves and Chernoff's Inequality
  • Contributor: Blyth, Stephen
  • imprint: Blackwell Publishers, 1993
  • Published in: Scandinavian Journal of Statistics
  • Language: English
  • ISSN: 0303-6898; 1467-9469
  • Origination:
  • Footnote:
  • Description: <p>The relationship between the correlation curve and the Pearson correlation ratio is investigated. Behaviour of the correlation curve is found to characterize the normal distribution in a natural manner. The correlation curve attains the value of the Pearson correlation ratio for all joint distributions of (X, Y) such that X is marginally normal. Conversely, if the correlation curve attains the value of the correlation ratio for all joint distributions of (X, Y) such that X is marginally distributed with law F, then F is normal. Chernoff's inequality proves central to these relationships.</p>