# Maximum order relation between univariate functional data

### Description

This function implements an order relation between univariate functional data based on the maximum relation, that is to say a pre-order relation obtained by comparing the maxima of two different functional data.

### Usage

1 | ```
max_ordered(fData, gData)
``` |

### Arguments

`fData` |
the first univariate functional dataset containing elements to
be compared, in form of |

`gData` |
the second univariate functional dataset containing elements to
be compared, in form of |

### Details

Given a univariate functional dataset, *X_1(t), X_2(t), …, X_N(t)*
and another functional dataset *Y_1(t),* *Y_2(t), …, Y_M(t)*
defined over the same compact interval *I=[a,b]*, the function computes
the maxima in both the datasets, and checks whether the first ones are lower
or equal than the second ones.

By default the function tries to compare each *X_i(t)* with the
corresponding *Y_i(t)*, thus assuming *N=M*, but when either *N=1*
or *M=1*, the comparison is carried out cycling over the dataset with
fewer elements. In all the other cases (*N\neq M,* and either
*N \neq 1* or *M \neq 1*) the function stops.

### Value

The function returns a logical vector of length *\max(N,M)* containing the
value of the predicate for all the corresponding elements.

### References

Valencia, D., Romo, J. and Lillo, R. (2015). A Kendall correlation
coefficient for functional dependence,
*Universidad Carlos III de Madrid technical report*,
`http://EconPapers.repec.org/RePEc:cte:wsrepe:ws133228`

.

### See Also

`maxima`

, `minima`

, `fData`

,
`area_ordered`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 | ```
P = 1e2
grid = seq( 0, 1, length.out = P )
Data_1 = matrix( c( 1 * grid,
2 * grid ),
nrow = 2, ncol = P, byrow = TRUE )
Data_2 = matrix( 3 * ( 0.5 - abs( grid - 0.5 ) ),
nrow = 1, byrow = TRUE )
Data_3 = rbind( Data_1, Data_1 )
fD_1 = fData( grid, Data_1 )
fD_2 = fData( grid, Data_2 )
fD_3 = fData( grid, Data_3 )
max_ordered( fD_1, fD_2 )
max_ordered( fD_2, fD_3 )
``` |