convex2COP

The convex composition of two copulas (Joe, 2014, p. 155) provides for some simple complexity extension between copula families. Let $\mathbf{A}$ and $\mathbf{B}$ be copulas with respective vectors of parameters $\Theta_\mathbf{A}$ and $\Theta_\mathbf{B}$, then the convex combination of these copulas is
$$\mathbf{C}^{\times}_{\alpha}(u,v) = \alpha\cdot\mathbf{A}(u, v; \Theta_\mathbf{A}) - (1-\alpha)\cdot\mathbf{B}(u,v; \Theta_\mathbf{B})\mbox{,}$$
where $0 \le \alpha \le 1$. The generalization of this function for $N$ number of copulas is provided by <code>convexCOP</code>.

copula composition

copula composition (convex combination)

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

convex2COP 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); and</dd> <dt>...</dt>
<dd>Additional arguments to pass to the copula.</dd></dl>

Arguments

Author

Convex Combination of Two Copulas — convex2COP

<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); and</dd>

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

</dl>

convex2COP: Convex Combination of Two Copulas

Description

Usage

Value

Arguments

Author

References

See Also