breveCOP

Adding permutation asymmetry (Chang and Joe, 2020, p. 1596) (<code>isCOP.permsym</code>) is simple for a bivariate copula family. Let $\mathbf{C}$ be a copula with respective vectors of parameters $\Theta_\mathbf{C}$, then the permutation asymmetry is added through an asymmetry parameter $\beta \in (-1, +1)$ by
$$\breve{\mathbf{C}}_{\beta;\Theta}(u,v) = v^{-\beta}\cdot\mathbf{C}(u, v^{(1+\beta)};\Theta)\mbox{, and}$$
for $0 \le \beta \le +1$ by
$$\breve{\mathbf{C}}_{\beta;\Theta}(u,v) = u^{+\beta}\cdot\mathbf{C}(u^{(1-\beta)}, v;\Theta)\mbox{.}$$
The parameter $\beta$ clashes in name and symbology with a parameter used by functions <code>composite1COP</code>, <code>composite2COP</code>, and <code>composite3COP</code>. As a result, support for alternative naming is provided for compatibility.

copula composition

permutation asymmetry

copula composition (permutation asymmetric)

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

breveCOP 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);</dd> <dt>breve</dt>
<dd>An alternative way from <code>para</code> to set the $\beta$ for this function; and</dd> <dt>...</dt>
<dd>Additional arguments to pass to the copula.</dd></dl>

Arguments

Author

Add Asymmetry to a Copula — breveCOP

<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);</dd>

 <dt>breve</dt>
<dd>An alternative way from <code>para</code> to set the $\beta$ for this function; and</dd>

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

</dl>

breveCOP: Add Asymmetry to a Copula

Description

Usage

Value

Arguments

Author

References

See Also