HAIRPINcop: The Hairpin Copula

In copBasic: General Bivariate Copula Theory and Many Utility Functions

The Hairpin Copula

Description

The Hairpin copula (Durante et al., 2014) is

\mathbf{C}_{\Theta}(u,v) = \mathbf{HAIRPIN}(u,v) = \mathrm{min}\bigl[u, v, \mathrm{mean}\bigl(f(u,v) \bigr) \bigr]\mbox{,}

as vectorized for the pairs (u_i, v_i) for i \in 1,2,\cdots, and f(x) = \alpha x^\phi, 1 \le \alpha \le \infty, and 1 \le \phi \le 2. The copula, as \alpha \rightarrow \infty or \phi \rightarrow 1 limits, to the comonotonicity coupla (\mathbf{M}(u,v); M).

Usage

HAIRPINcop(u, v, para=c(1, 2, 1), ...)

Arguments

u	Nonexceedance probability u in the X direction;
v	Nonexceedance probability v in the Y direction;
para	A vector (three element) of two parameters and the reflection: \alpha and \phi of the coupla then the reflection number n \in 1, 2, 3, 4 following the reflection pattern of COP; and
...	Additional arguments to pass.

Value

Value(s) for the copula are returned.

Author(s)

W.H. Asquith

References

Durante, F., Fernández-Sánchez, J., and Trutschnig, W., 2014, Multivariate copulas with hairpin support: Journal of Multivariate Analysis, v. 130, pp. 323–334, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.jmva.2014.06.009")}.

See Also

M

Examples

## Not run: 
  # Produce a Celtic Knot look through simulation -----------------------------
  nsim <- 1.5E4
  plot(c(0, 1), c(0, 1), type="n", bty="n",
       xaxt="n", yaxt="n", xaxs="r", yaxs="r", xlab="", ylab="")
  sapply(1:4, function(n) {
                  UV <- simCOP(nsim, cop=HAIRPINcop, para=c(1.12, 1.8, n),
                 seed=1, ploton=FALSE, pch=16, cex=0.6, col=n); return(n) })
  sapply(1:4, function(n) {
                  UV <- simCOP(nsim, cop=HAIRPINcop, para=c(1.12, 1.3, n),
                 seed=1, ploton=FALSE, pch=16, cex=0.6, col=n); return(n) }) # 
## End(Not run)

copBasic documentation built on July 23, 2026, 1:07 a.m.