W: The Fréchet-Hoeffding Lower-Bound Copula

In copBasic: General Bivariate Copula Theory and Many Utility Functions

The Fréchet–Hoeffding Lower-Bound Copula

Description

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

\mathbf{W}(u,v) = \mathrm{max}(u+v-1,0)\mbox{.}

This is the copula of perfect anti-association (countermonotonicity, perfectly negative dependence) between U and V and is sometimes referred to as the countermonotonicity copula. Its opposite is the \mathbf{M}(u,v) copula (comonotonicity copula; M), and statistical independence is the \mathbf{\Pi}(u,v) copula (P).

Usage

W(u, v, ...)

Arguments

u	Nonexceedance probability u in the X direction;
v	Nonexceedance probability v in the Y direction; and
...	Additional arguments to pass.

Value

Value(s) for the copula are returned.

Author(s)

W.H. Asquith

References

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

See Also

M, P

Examples

W(0.41, 0.60) # just barely touching the support, so small, 0.01
W(0.25, 0.45) # no contact with the support, so 0
W(1,    1   ) # total consumption of the support, so 1

copBasic documentation built on June 28, 2025, 1:08 a.m.