PLACKETTpar: Estimate the Parameter of the Plackett Copula
Description
The parameter $\Theta$ of the Plackett Copula is related to Spearman's Rho ($\rho_S \ne 1$)
$$\rho_S(\Theta) = \frac{\Theta + 1}{\Theta - 1} - \frac{2\Theta\log(\Theta)}{(\Theta - 1)^2}$$
and a median split estimator best shown in code. First, compute the two medians medx <- median(x); medy <- median(y). Second, compute the number of occurrences where both values are less than their medians k <- length(x[x < medx & y < medy]). Third, express this as a probability m <- k/length(x), and finally compute the $\Theta$ by
$$\Theta = \frac{4m^2}{(1-2m)^2}$$
Usage
PLACKETTpar(x, y, rho=NULL, byrho=FALSE, ...)
Arguments
x
Vector of values for variable X,
y
Vector of values for variable Y,
rho
Spearman's Rho and byrho is set to TRUE automatically,
byrho
Should Spearman's Rho be used instead of median split, and
...
Additional arguments to pass.
Value
A value for $\Theta$ is returned.
References
Nelson, R.B., 2006, An introduction to copulas: New York, Springer, 269 p.
Salvadori, G., De Michele, C., Kottegoda, N.T., and Rosso, R., 2007, Extremes in nature---An approach using copulas: Dordrecht, Netherlands, Springer, Water Science and Technology Library 56, 292 p.