PSP {copBasic}R Documentation

The Ratio of the Product Copula to Summation minus Product Copula

Description

Compute PSP copula (Nelsen, 2006, p. 23) is named by the author (Asquith) for the copBasic package and is

PSP(u,v)=ΠΣΠ=uvu+vuv\mbox,\mathbf{PSP}(u,v) = \frac{\mathbf{\Pi}}{\mathbf{\Sigma} - \mathbf{\Pi}} = \frac{uv}{u + v - uv}\mbox{,}

where Π\mathbf{\Pi} is the indpendence or product copula (P) and Σ\mathbf{\Sigma} is the sum Σ=u+v\mathbf{\Sigma} = u + v. The PSP(u,v)\mathbf{PSP}(u,v) copula is a special case of the N4212(u,v)\mathbf{N4212}(u,v) copula (N4212cop). The PSP\mathbf{PSP} is included in copBasic because of its simplicity and for pedagogical purposes. The name “PSP” comes from “Product, Summation, Product” to loosely reflect the mathematical formula shown. Nelsen (2006, p. 114) notes that the PSP copula shows up in several families and designates it as “Π/(ΣΠ)\mathbf{\Pi}/(\mathbf{\Sigma}-\mathbf{\Pi}).” The PSP is undefined for u=v=0u = v = 0 but no internal trapping is made; calling functions will have to intercept the NaN so produced for {0,0}\{0, 0\}. The PSP\mathbf{PSP} is left internally untrapping NaN so as to be available to stress other copula utility functions within the copBasic package.

Usage

PSP(u, v, ...)

Arguments

u

Nonexceedance probability uu in the XX direction;

v

Nonexceedance probability vv in the YY direction; and

...

Additional arguments to pass, which for this copula are not needed, but given here to support flexible implementation.

Value

Value(s) for the copula are returned.

Author(s)

W.H. Asquith

References

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

See Also

P, N4212cop

Examples

PSP(0.4,0.6)
PSP(0,0)
PSP(1,1)

[Package copBasic version 2.2.4 Index]