This function computes the Modified Hypograph Index (MEI) of elements of a univariate functional dataste.
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Data |
either an |
Given a univariate functional dataset, X_1(t), X_2(t), …, X_N(t), defined over a compact interval I=[a,b], this function computes the MHI, i.e.:
MHI( X(t) ) = \frac{1}{N} ∑_{i=1}^N \tilde{λ}( X(t) ≥q X_i(t) ),
where \tilde{λ}(\cdot) is the normalised Lebesgue measure over I=[a,b], that is \tilde{λ(A)} = λ( A ) / ( b - a ).
The function returns a vector containing the values of MHI for each
element of the functional dataset provided in Data
.
Lopez-Pintado, S. and Romo, J. (2012). A half-region depth for functional data, Computational Statistics and Data Analysis, 55, 1679-1695.
Arribas-Gil, A., and Romo, J. (2014). Shape outlier detection and visualization for functional data: the outliergram, Biostatistics, 15(4), 603-619.
HI
, MEI
, EI
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fData
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