pord_spread: Compare Spread of Vectors (Preorder)
In agop: Aggregation Operators and Preordered Sets

Description Usage Arguments Details Value References See Also

This function determines whether one numeric vector has not greater spread than the other

1	pord_spread(x, y, incompatible_lengths = NA)

`x`	numeric vector
`y`	numeric vector of the same length as `x`
`incompatible_lengths`	single logical value, value to return iff lengths of `x` and `y` differ

We say that x of size n is of no greater spread than y iff for all i,j=1,…,n such that x_i>x_j it holds x_i-x_j≤ y_i-y_jll . Such a preorder is used in the definition of a spread measure (see Gagolewski, 2015).

Note that the class of dispersion functions includes e.g. the sample variance (see var), standard veriation (see sd), range (see range and then diff), interquartile range (see IQR), median absolute deviation (see mad).

The function returns a single logical value, which states whether x has no greater spread than y

Gagolewski M., Spread measures and their relation to aggregation functions, European Journal of Operational Research 241(2), 2015, pp. 469–477.

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: check_comonotonicity, pord_nd, 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