copBasic (version 2.0.1)

M: The Fréchet{Frechet}-Hoeffding Upper Bound Copula

Description

Compute the Fréchet{Frechet}-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; W), and statistical independence is the $\mathbf{\Pi}(u,v)$ copula (P).

Usage

M(u, v, ...)

Arguments

u

Nonexceedance probability $u$ in the $X$ direction;

v

Nonexceedance probability $v$ in the $Y$ direction; and

...

Additional arguments to pass.

Value

• Value(s) for the copula are returned.

encoding

utf8

concept

• Frechet upper bound copula
• Frechet-Hoeffding upper bound copula
• Frechet upper bound
• Frechet-Hoeffding upper bound

References

Nelsen, R.B., 2006, An introduction to copulas: New York, Springer, 269 p.

See Also

W, P

Examples

M(0.4,0.6)
M(0,0)
M(1,1)