glueCOP

The gluing copula technique (Erdely, 2017, p. 71), given two bivariate copulas $\mathbf{C}_A$ and $\mathbf{C}_B$ and a fixed value $0 \le \gamma \le 1$ is
$$\mathbf{C}_{\gamma}(u,v) = \gamma\cdot\mathbf{C}_A(u/\gamma, v)$$
for $0 \le u \le \gamma$ and
$$\mathbf{C}_{\gamma}(u,v) = (1-\gamma)\cdot\mathbf{C}_B((u-\gamma)
\,/\,(1-\gamma), v)$$
for $\gamma \le u \le 1$ and $\gamma$ represents the gluing point in $u$ (horizontal axis). The logic is simply the rescaling of $\mathbf{C}_A$ to $[0,\gamma] \times [0,1]$ and $\mathbf{C}_B$ to $[\gamma,1] \times [0,1]$. Copula gluing is potentially useful in circumstances for which regression is non-monotone.

copula (formulas)

copula composition

copula gluing

Erdely (2017) Examples and Exercises

Extensive functions for bivariate copula (bicopula) computations and related operations
for bicopula theory. The lower, upper, product, and select other bicopula are implemented along
with operations including the diagonal, survival copula, dual of a copula, co-copula, and
numerical bicopula density. Level sets, horizontal and vertical sections are supported. Numerical
derivatives and inverses of a bicopula are provided through which simulation is implemented.
Bicopula composition, convex combination, asymmetry extension, and products also are provided.
Support extends to the Kendall Function as well as the Lmoments thereof. Kendall Tau,
Spearman Rho and Footrule, Gini Gamma, Blomqvist Beta, Hoeffding Phi, Schweizer-
Wolff Sigma, tail dependency, tail order, skewness, and bivariate Lmoments are implemented, and
positive/negative quadrant dependency, left (right) increasing (decreasing) are available.
Other features include Kullback-Leibler Divergence, Vuong Procedure, spectral measure, and
Lcomoments for inference, maximum likelihood, and AIC, BIC, and RMSE for goodness-of-fit.

William Asquith

copBasic

General Bivariate Copula Theory and Many Utility Functions

glueCOP function

<dl> <dt>u</dt>
<dd>Nonexceedance probability $u$ in the $X$ direction;</dd> <dt>v</dt>
<dd>Nonexceedance probability $v$ in the $Y$ direction;</dd> <dt>para</dt>
<dd>A special parameter <code>list</code> (see Note) with a mandatory element of <code>glue</code> parameter $\gamma$; and</dd> <dt>...</dt>
<dd>Additional arguments to pass to the copulas.</dd></dl>

Arguments

Author

Gluing Two Copulas — glueCOP

<dl>

 <dt>u</dt>
<dd>Nonexceedance probability $u$ in the $X$ direction;</dd>

 <dt>v</dt>
<dd>Nonexceedance probability $v$ in the $Y$ direction;</dd>

 <dt>para</dt>
<dd>A special parameter <code>list</code> (see Note) with a mandatory element of <code>glue</code> parameter $\gamma$; and</dd>

 <dt>...</dt>
<dd>Additional arguments to pass to the copulas.</dd>

</dl>

glueCOP: Gluing Two Copulas

Description

Usage

Value

Arguments

Author

References

See Also