pord_spread {agop} | R Documentation |

## Compare Spreads of Vectors (Preorder)

### Description

These functions determine whether one numeric vector has not greater spread than the other

### Usage

pord_spread(x, y) pord_spreadsym(x, y)

### Arguments

`x` |
numeric vector |

`y` |
numeric vector of the same length as |

### Details

These functions accept only vectors of the same size.
[TO DO: should not it return `FALSE`

or `NA`

in this case?]

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
dispersion functions (see Gagolewski, 2013)
and is implemented in `pord_spread`

,

Moreover, `pord_spreadsym`

implements
the relation corresponding to symmetrized dispersion
functions, i.e. which acts on sorted vectors.

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 (MAD).

### Value

Both functions return a single logical value,
which states whether `x`

has no greater
spread than `y`

### References

Gagolewski M., *Dispersion Functions: Aggregation Operators that
Measure Variability, Spread, or Scatter of Numeric Sequences*,
submitted paper, 2013.

Gagolewski M., *Symmetric Dispersion Functions*, in preparation, 2013.

### See Also

Other binary_relations: `check_comonotonicity`

;
`pord_weakdom`

;
`rel_closure_reflexive`

,
`rel_is_reflexive`

,
`rel_reduction_reflexive`

;
`rel_closure_symmetric`

,
`rel_is_symmetric`

;
`rel_closure_total_fair`

,
`rel_is_total`

;
`rel_closure_transitive`

,
`rel_is_transitive`

,
`rel_reduction_hasse`

,
`rel_reduction_transitive`

;
`rel_graph`

;
`rel_is_antisymmetric`

;
`rel_is_asymmetric`

;
`rel_is_cyclic`

;
`rel_is_irreflexive`

Other dispersion_functions: `d2owa`

,
`d2owa_checkwts`

*agop*version 0.2-0 Index]