copBasic (version 2.2.7)

W: The Fréchet--Hoeffding Lower-Bound Copula

Description

Compute the Fréchet--Hoeffding lower-bound copula (Nelsen, 2006, p. 11), which is defined as $$\mathbf{W}(u,v)=\max (u+v-1,0)\text{.}$$ 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.

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