derCOPinv2

Compute the inverse of a numerical partial derivative for $U$ with respect to $V$ of a copula, which is a conditional quantile function for nonexceedance probability $t$, or
$$t = c_v(u) = \mathbf{C}^{(-1)}_{1 \mid 2}(u \mid v) = \frac{\delta \mathbf{C}(u,v)}{\delta v}\mbox{,}$$
and solving for $u$. Nelsen (2006, pp. 13, 40--41) shows that this inverse is quite important for random variable generation using the conditional distribution method. This function is not vectorized and will not be so.

derivative

copula operator

copula (conditional quantile function)

copula (utility)

copula (derivative inverse)

conditional quantile function

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

derCOPinv2 function

<dl> <dt>cop</dt>
<dd>A copula function;</dd> <dt>v</dt>
<dd>A single nonexceedance probability $v$ in the $Y$ direction;</dd> <dt>t</dt>
<dd>A single nonexceedance probability level $t$;</dd> <dt>trace</dt>
<dd>A logical controlling a <code>message</code> on whether the signs on the <code>uniroot</code> are the same---this is helpful in exploring the numerical derivative limits of a given implementation of a copula.</dd> <dt>delv</dt>
<dd>The $\Delta v$ interval for the derivative;</dd> <dt>para</dt>
<dd>Vector of parameters or other data structure, if needed, to pass to <code>cop</code>; and</dd> <dt>...</dt>
<dd>Additional arguments to pass to the copula.</dd></dl>

Arguments

Author

Numerical Derivative Inverse of a Copula for U with respect to V — derCOPinv2

<dl>

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

 <dt>v</dt>
<dd>A single nonexceedance probability $v$ in the $Y$ direction;</dd>

 <dt>t</dt>
<dd>A single nonexceedance probability level $t$;</dd>

 <dt>trace</dt>
<dd>A logical controlling a <code>message</code> on whether the signs on the <code>uniroot</code> are the same---this is helpful in exploring the numerical derivative limits of a given implementation of a copula.</dd>

 <dt>delv</dt>
<dd>The $\Delta v$ interval for the derivative;</dd>

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

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

</dl>

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derCOPinv2: Numerical Derivative Inverse of a Copula for U with respect to V

Description

Usage

Value

Arguments

Author

References

See Also