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, ...)
Value
Value(s) for the copula are returned.
Arguments
u
Nonexceedance probability \(u\) in the \(X\) direction;
v
Nonexceedance probability \(v\) in the \(Y\) direction; and
...
Additional arguments to pass.
Author
W.H. Asquith
References
Nelsen, R.B., 2006, An introduction to copulas: New York, Springer, 269 p.
W(0.41, 0.60) # just barely touching the support, so small, 0.01W(0.25, 0.45) # no contact with the support, so 0W(1, 1 ) # total consumption of the support, so 1