W: The Fréchet{Frechet}-Hoeffding Lower Bound Copula
Description
Compute the Fréchet{Frechet}-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.
encoding
utf8
concept
Frechet upper bound copula
Frechet-Hoeffding upper bound copula
Frechet upper bound
Frechet-Hoeffding upper bound
References
Nelsen, R.B., 2006, An introduction to copulas: New York, Springer, 269 p.