Dependence Properties of B-Spline Copulas

Xiaoling Dou*, Satoshi Kuriki, Gwo Dong Lin, Donald Richards

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


We construct by using B-spline functions a class of copulas that includes the Bernstein copulas arising in Baker’s distributions. The range of correlation of the B-spline copulas is examined, and the Fréchet–Hoeffding upper bound is proved to be attained when the number of B-spline functions goes to infinity. As the B-spline functions are well-known to be an order-complete weak Tchebycheff system from which the property of total positivity of any order follows for the maximum correlation case, the results given here extend classical results for the Bernstein copulas. In addition, we derive in terms of the Stirling numbers of the second kind an explicit formula for the moments of the related B-spline functions on the right half-line.

Original languageEnglish
Pages (from-to)283-311
Number of pages29
JournalSankhya A
Issue number1
Publication statusPublished - 2021 Feb
Externally publishedYes


  • 41A15
  • 62G30
  • Bernstein copula
  • Fréchet–Hoeffding upper bound
  • Order-complete weak Tchebycheff system
  • Primary 62H20
  • Schur function
  • Stirling number of the second kind
  • Total positivity of order r

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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