This function computes the Band Depth (BD) of elements of a functional dataset.
1 2 3 4 5 6 7 
Data 
either an object of class 
Given a univariate functional dataset, X_1(t), X_2(t), …, X_N(t), this function computes the sample BD of each element with respect to the other elements of the dataset, i.e.:
BD( X( t ) ) = {N \choose 2 }^{1} ∑_{1 ≤q i_1 < i_2 ≤q N} I( G(X) \subset B( X_{i_1}, X_{i_2} ) ),
where G(X) is the graphic of X(t), B(X_{i_1},X_{i_2}) is the envelope of X_{i_1}(t) and X_{i_2}(t), and X \in ≤ft\{X_1, …, X_N\right\}.
See the References section for more details.
The function returns a vector containing the values of BD for the given dataset.
LopezPintado, S. and Romo, J. (2009). On the Concept of Depth for Functional Data, Journal of the American Statistical Association, 104, 718734.
LopezPintado, S. and Romo. J. (2007). Depthbased inference for functional data, Computational Statistics & Data Analysis 51, 49574968.
MBD
, BD_relative
,
MBD_relative
, fData
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16  grid = seq( 0, 1, length.out = 1e2 )
D = matrix( c( 1 + sin( 2 * pi * grid ),
0 + sin( 4 * pi * grid ),
1  sin( pi * ( grid  0.2 ) ),
0.1 + cos( 2 * pi * grid ),
0.5 + sin( 3 * pi + grid ),
2 + sin( pi * grid ) ),
nrow = 6, ncol = length( grid ), byrow = TRUE )
fD = fData( grid, D )
BD( fD )
BD( D )

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