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The Kendall and Spearman rank correlations of the bivariate skew normal distribution

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  • Andréas Heinen
  • Alfonso Valdesogo

Abstract

We derive the Kendall and Spearman rank correlation coefficients of the bivariate skew normal (SN) distribution. For a given correlation parameter, we provide conditions on the shape parameters, under which the SN is more dependent than the normal in terms of each of the two‐rank correlations. We further show how our results can be used for rank‐based estimation procedures of the correlation parameter and the equal shape parameter of the SN, whose consistency and asymptotic normality we establish.

Suggested Citation

  • Andréas Heinen & Alfonso Valdesogo, 2022. "The Kendall and Spearman rank correlations of the bivariate skew normal distribution," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(4), pages 1669-1698, December.
    • Handle: RePEc:bla:scjsta:v:49:y:2022:i:4:p:1669-1698
    DOI: 10.1111/sjos.12587
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    4. Heinen, Andréas & Valdesogo, Alfonso, 2020. "Spearman rank correlation of the bivariate Student t and scale mixtures of normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 179(C).
    5. Padoan, Simone A., 2011. "Multivariate extreme models based on underlying skew-t and skew-normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 102(5), pages 977-991, May.
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