PSP: 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 $$\mathbf{PSP}(u,v) = \frac{\mathbf{\Pi}}{\mathbf{\Sigma} - \mathbf{\Pi}} = \frac{uv}{u + v - uv}\mbox{,}$$ where $\mathbf{\Pi}$ is the indpendence or product copula (P) and $\mathbf{\Sigma}$ is the sum $\mathbf{\Sigma} = u + v$. The $\mathbf{PSP}(u,v)$ copula is a special case of the $\mathbf{N4212}(u,v)$ copula (N4212cop). The $\mathbf{PSP}$ 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 “$\mathbf{\Pi}/(\mathbf{\Sigma}-\mathbf{\Pi})$.” The PSP is undefined for $u = v = 0$ but no internal trapping is made; calling functions will have to intercept the NaN so produced for $\{0, 0\}$. The $\mathbf{PSP}$ is left internally untrapping NaN so as to be available to stress other copula utility functions within the copBasic package.

Usage

PSP(u, v, ...)

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

Author

W.H. Asquith

References

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

Examples

Run this code

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

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