surfuncCOP

Compute the joint survival function for a copula (Nelsen, 2006, p. 33), which is defined as
$$\overline{\mathbf{C}}(u,v) = \mathrm{Pr}[U &gt; u, V &gt; v] = 1 - u - v + \mathbf{C}(u,v) = \hat{\mathbf{C}}(1-u, 1-v)\mbox{,}$$
where $\hat{\mathbf{C}}(u',v')$ is the survival copula (<code>surCOP</code>), which is defined by
$$\hat{\mathbf{C}}(u',v') = \mathrm{Pr}[U &gt; u, V &gt; v] = u' + v' - 1 + \mathbf{C}(1-u',1-v')\mbox{.}$$
Although the joint survival function is an expression of the probability that both $U &gt; v$ and $U &gt; v$, $\overline{\mathbf{C}}(u,v)$ is not a copula.

copula operator

joint probability

conditional return period

Salvadori et al. (2007) 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

surfuncCOP 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>cop</dt>
<dd>A copula function;</dd> <dt>para</dt>
<dd>Vector of parameters or other data structure, if needed, to pass to the copula; and</dd> <dt>...</dt>
<dd>Additional arguments to pass (such as parameters, if needed, for the copula in the form of a list.</dd></dl>

Arguments

Author

The Joint Survival Function — surfuncCOP

<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>cop</dt>
<dd>A copula function;</dd>

 <dt>para</dt>
<dd>Vector of parameters or other data structure, if needed, to pass to the copula; and</dd>

 <dt>...</dt>
<dd>Additional arguments to pass (such as parameters, if needed, for the copula in the form of a list.</dd>

</dl>

surfuncCOP: The Joint Survival Function

Description

Usage

Value

Arguments

Author

References

See Also