blomatrixCOP: A Matrix of Blomqvist-like Betas of a Copula

Description

Compute the Blomqvist-like Betas matrix $\beta^\circ_\mathbf{C}$-matrix of a copula, which is defined at presumably strategic points within $\mathcal{I}^2$, as (for as.blomCOPss=FALSE argument)

$$\beta^\circ_\mathbf{C} = \frac{\mathbf{C}(u^\circ,v^\circ)}{\mathbf{\Pi}(1/2, 1/2)} - 1\mbox{,}$$

where the $u^\circ$ and $v^\circ$ are of two types of gridded locations in $\mathcal{I}^2$ space and if $u^\circ = 1/2$ and $v^\circ = 1/2$, then central location of the matrix is Blomqvist Beta (blomCOP). The definition of $\beta^\circ_\mathbf{C}$ is such that the matrix is entirely zero for the independence copula ($\mathbf{\Pi}(u,v)$) (P) when $\mathbf{C}(u^\circ,v^\circ) = \mathbf{\Pi}(u,v)$ at the medial location $u,v=1/2$. Also, the definition here might be unique to the copBasic package. The decile version (blomatrixCOPdec) of this function uses $u^\circ \in (1, 5, 9) / 10$ and $v^\circ \in (1, 5, 9) / 10$. Whereas, the quartile version (blomatrixCOPiqr) of this function uses $u^\circ \in (25, 50, 75) / 100$ and $v^\circ \in (25, 50, 75)/100$. If as.blomCOPss=TRUE argument is set (default operation), then the coordinate locations in the matrix become the $\beta^\diamond_\mathbf{C}$ of blomCOPss. As a rule $\beta^\circ_\mathbf{C} \ne \beta^\diamond_\mathbf{C}$.

Usage

blomatrixCOPdec(cop=NULL, para=NULL, as.sample=FALSE, as.blomCOPss=TRUE,
                  ctype=c("weibull", "hazen", "1/n",
                          "bernstein", "checkerboard"), ...)
blomatrixCOPiqr(cop=NULL, para=NULL, as.sample=FALSE, as.blomCOPss=TRUE,
                  ctype=c("weibull", "hazen", "1/n",
                          "bernstein", "checkerboard"), ...)

Value

The matrix for $\beta^\circ_\mathbf{C}$ is returned depending on whether the decile or quartile version has been called.

Arguments

cop: A copula function;
para: Vector of parameters or other data structure, if needed, to pass to the copula;
as.sample: A logical controlling whether an optional R data.frame in para is used to compute the $\hat\beta^\circ_\mathbf{C}$-matrix at which point the ctype argument will be passed to multiple calls of EMPIRcop;
as.blomCOPss: A logical to trigger blomCOPss for each of the $(u,v)$ locations where for the blomCOPss calls ($\beta^\diamond_\mathbf{C}(\mathbf{u}, \mathbf{v})$): $u \mapsto (u,u) \mapsto \mathbf{u}$ and $v \mapsto (v,v) \mapsto \mathbf{v}$;
ctype: Argument of the same as EMPIRcop; and
...: Additional arguments to pass to the copula.

Author

W.H. Asquith

Description

Usage

Value

Arguments

Author

See Also