copBasic (version 1.5.0)

N4.2.12cop: The Copula of Equation 4.2.12 of Nelson's Book

Description

The N4.2.12 Copula is $$\mathbf{C}_{\Theta}(u,v) = (1 + [(u^{-1} -1)^\Theta + (v^{-1} -1)^\Theta]^{1/\Theta})^{-1}$$

The N4.2.12 Copula is not comprehensive because $\Theta = 0$ the copula becomes $\mathbf{PSP}(u,v)$(PSP), as $\Theta \rightarrow \infty$ the copula becomes $\mathbf{M}(u,v)$ (M). The copula is undefined for $\Theta < 1$. The N4.2.12 Copula has respective lower and upper tail dependency and the simCOP examples in this documentation will show.

Usage

N4.2.12cop(u, v, para=NULL, infis=100, ...)

Arguments

u

A nonexceedance probability in X direction,

v

A nonexceedance probability in Y direction,

para

A vector (single element) of parameters---the $\Theta$ parameter,

infis

What is infinity? Testing shows that > 100 is about right to consider the copula as becoming $\mathbf{M}(u,v)$ (M), and

...

Additional arguments to pass.

Value

• The value for the copula is returned.

References

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

Examples

N4.2.12cop(0.4,0.6,para=1)
PSP(0.4,0.6) # same two values


N4.2.12cop(0.4,0.6,para=10)

D <- simCOP(n=400, cop=N4.2.12cop, para=2)
D <- simCOP(n=400, cop=N4.2.12cop, para=10)
D <- simCOP(n=400, cop=N4.2.12cop, para=100)