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copBasic (version 1.6.0)

blomCOP: The Blomqvist's Beta of a Copula

Description

Compute the Blomqvist's Beta $\beta_\mathbf{C}$ of a copula (Nelson, 2006, p. 182), which is defined at the middle of $\mathcal{I}^2$ as

$$\beta_\mathbf{C} = 4\times\mathbf{C}\biggl(\frac{1}{2},\frac{1}{2}\biggr) - 1\mbox{,}$$

where the $u = v = 1/2$ and thus shows that $\beta_\mathbf{C}$ is based on the median joint probability. Nelson also reports that although, Blomqvist's Beta depends only on the copula only through its value at the center of $[0,1]\times[0,1]$, it nevertheless often provides an accurate approximation to Spearman's Rho rhoCOP and Kendall's Tau tauCOP.

Usage

blomCOP(cop=NULL, para=NULL, ...)

Arguments

cop
A copula function;
para
Vector of parameters or other data structure, if needed, to pass to the copula; and
...
Additional arguments to pass to the copula.

Value

  • The value for $\beta_\mathbf{C}$ is returned.

References

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

See Also

giniCOP, rhoCOP, tauCOP

Examples

Run this code
blomCOP(cop=PSP)

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