agop (version 0.2-2)

check_comonotonicity: Check If Two Vectors Are Comonotonic

Description

This functions determines if two vectors have a common ordering permutation.

Usage

check_comonotonicity(x, y, incompatible_lengths = NA)

Arguments

x

numeric vector

y

numeric vector

incompatible_lengths

single logical value, value to return iff lengths of x and y differ

Value

Returns a single logical value.

Details

Two vectors x, y of equal length \(n\) are comonotonic, if and only if there exists a permutation \(\sigma\) such that \(x_{\sigma(1)}\le \dots \le x_{\sigma(n)}\) and \(y_{\sigma(1)}\le \dots \le y_{\sigma(n)}\). Thus, \(\sigma\) orders x and y simultaneously. Equivalently, x and y are comonotonic, iff \((x_i-x_j)(y_i-y_j)\ge 0\) for every i,j.

If there are missing values in x or y, the function returns NA.

Currently, the algorithm implemented has \(O(n^2)\) time complexity.

References

Grabisch M., Marichal J.-L., Mesiar R., Pap E., Aggregation functions, Cambridge University Press, 2009.

Gagolewski M., Data Fusion: Theory, Methods, and Applications, Institute of Computer Science, Polish Academy of Sciences, 2015, 290 pp. isbn:978-83-63159-20-7

See Also

Other binary_relations: pord_nd, pord_spread, pord_weakdom, rel_graph, rel_is_antisymmetric, rel_is_asymmetric, rel_is_cyclic, rel_is_irreflexive, rel_is_reflexive, rel_is_symmetric, rel_is_total, rel_is_transitive, rel_reduction_hasse