kfuncCOPinv

Compute the (numerical) inverse \(F^{(-1)}_K(z) \equiv z(F_K)\) of the Kendall Function \(F_K(z; \mathbf{C})\) (<code>kfuncCOP</code>) of a copula \(\mathbf{C}(u,v)\) given nonexceedance probability \(F_K\). The \(z\) is the joint probability of the random variables \(U\) and \(V\) coupled to each other through the copula \(\mathbf{C}(u,v)\) and the nonexceedance probability of the probability \(z\) is \(F_K\)---statements such as ``probabilities of probabilities'' are rhetorically complex so pursuit of word precision is made herein.

copula (properties)

Kendall inverse distribution function

Kendall quantile function

copula (characteristics)

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, 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

kfuncCOPinv function

<dl> <dt>f</dt>
<dd>Nonexceedance probability \((0 \le F_K \le 1)\);</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.</dd></dl>

Arguments

Author

The Inverse Kendall Function of a Copula — kfuncCOPinv

<dl>

 <dt>f</dt>
<dd>Nonexceedance probability \((0 \le F_K \le 1)\);</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.</dd>

</dl>

kfuncCOPinv: The Inverse Kendall Function of a Copula

Description

Usage

Value

Arguments

Author

References

See Also