M: The Fréchet-Hoeffding Upper-Bound Copula

In wasquith/copBasic: General Bivariate Copula Theory and Many Utility Functions

The Fréchet–Hoeffding Upper-Bound Copula

Description

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; 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.

Author(s)

W.H. Asquith

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)

wasquith/copBasic documentation built on March 10, 2024, 11:24 a.m.