check_comonotonicity {agop} R Documentation

## 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

### 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 implemented algorithm has O(n^2) time complexity.

### Value

Returns a single logical value.

### 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

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()