copBasic (version 2.1.5)

W: The Fr<U+00E9>chet--Hoeffding Lower Bound Copula

Description

Compute the Fr<U+00E9>chet--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.

References

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

See Also

M, P

Examples

# NOT RUN {
W(0.4,0.6)
W(0,0)
W(1,1)
# }