Compute the Fréchet--Hoeffding upper-bound copula (Nelsen, 2006, p. 11), which is defined as
$$\mathbf{M}(u,v) = \mathrm{min}(u,v)\mbox{.}$$
This is the copula of perfect association (comonotonicity, perfectly positive dependence) between $U$ and $V$ and is sometimes referred to as the comonotonicity copula. Its opposite is the $\mathbf{W}(u,v)$ copula (countermonotonicity copula; <code>W</code>), and statistical independence is the $\mathbf{\Pi}(u,v)$ copula (<code>P</code>).

copula

copula (formulas)

copula (limits/bounds)

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

M 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; and</dd> <dt>...</dt>
<dd>Additional arguments to pass.</dd></dl>

Arguments

Author

The Fréchet--Hoeffding Upper-Bound Copula — M

<dl>

 <dt>u</dt>
<dd>Nonexceedance probability $u$ in the $X$ direction;</dd>

 <dt>v</dt>
<dd>Nonexceedance probability $v$ in the $Y$ direction; and</dd>

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

</dl>

M: The Fréchet--Hoeffding Upper-Bound Copula

Description

Usage

Value

Arguments

Author

References

See Also

Examples