| 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 |
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
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()