This method computes the sample median of a univariate functional dataset based on a definition of depth for univariate functional data.

1 | ```
median_fData(fData, type = "MBD", ...)
``` |

`fData` |
the univariate functional dataset whose
median is required, in form of |

`type` |
a string specifying the name of the function defining the depth
for univariate data to be used. It must be a valid name of a function defined
in the current environment, default is |

`...` |
additional parameters to be used in the function specified by
argument |

Provided a definition of functional depth for univariate data,
the corresponding median (i.e. the deepest element of the sample) is returned as the desired median.
This method does **not** coincide with the computation of the
cross-sectional median of the sample of the point-by-point measurements on
the grid. Hence, the sample median is a member of the dataset provided.

The function returns a `fData`

object containing the desired
sample median.

`fData`

, `mean.fData`

,
`median_mfData`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | ```
N = 1e2
P = 1e2
grid = seq( 0, 1, length.out = P )
# Generating a gaussian functional sample with desired mean
# Being the distribution symmetric, the sample mean and median are coincident
target_median = sin( 2 * pi * grid )
C = exp_cov_function( grid, alpha = 0.2, beta = 0.2 )
fD = fData( grid, generate_gauss_fdata( N,
centerline = target_median,
Cov = C ) )
# Graphical representation of the mean
plot( fD )
plot( median_fData( fD ), col = 'black', lwd = 2, lty = 2, add = TRUE )
``` |

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