M function

The --Hoeffding Upper-Bound Copula

The --Hoeffding Upper-Bound Copula

Compute the --Hoeffding upper-bound copula (Nelsen, 2006, p. 11), which is defined as [REMOVE_ME]M(u,v)=min(u,v)\mbox.[REMOVEME2] \mathbf{M}(u,v) = \mathrm{min}(u,v)\mbox{.} [REMOVE_ME_2]

This is the copula of perfect association (comonotonicity, perfectly positive dependence) between UU and VV and is sometimes referred to as the comonotonicity copula. Its opposite is the W(u,v)\mathbf{W}(u,v) copula (countermonotonicity copula; W), and statistical independence is the Π(u,v)\mathbf{\Pi}(u,v) copula (P). utf8

Description

Compute the --Hoeffding upper-bound copula (Nelsen, 2006, p. 11), which is defined as

M(u,v)=min(u,v)\mbox. \mathbf{M}(u,v) = \mathrm{min}(u,v)\mbox{.}

This is the copula of perfect association (comonotonicity, perfectly positive dependence) between UU and VV and is sometimes referred to as the comonotonicity copula. Its opposite is the W(u,v)\mathbf{W}(u,v) copula (countermonotonicity copula; W), and statistical independence is the Π(u,v)\mathbf{\Pi}(u,v) copula (P).

M(u, v, ...)

Arguments

  • u: Nonexceedance probability uu in the XX direction;
  • v: Nonexceedance probability vv in the YY direction; and
  • ...: Additional arguments to pass.

Returns

Value(s) for the copula are returned.

References

Nelsen, R.B., 2006, An introduction to copulas: New York, Springer, 269 p.

Author(s)

W.H. Asquith

See Also

W, P

Examples

M(0.4,0.6) M(0,0) M(1,1)
  • Maintainer: William Asquith
  • License: GPL-2
  • Last published: 2024-10-08

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