measureDispersion: Dispersion of Ensemble Members

In xemd: eXtended Empirical Mode Decomposition

Dispersion of Ensemble Members

Description

Computes, sample by sample and mode by mode, the sample variance of the members of an ensemble around their mean, and that sample variance divided by the number of members. The latter estimates the variance of the mean under the assumptions stated below.

Usage

measureDispersion(realizations)

Arguments

realizations

Finite numeric array with three dimensions, samples by modes by realizations, with at least two realizations. The modes of each realization occupy their extraction order, and a mode absent from a realization is filled with zeros.

Details

With M realizations C^{(m)} and their mean \bar C, the sample variance is

s^2 = \frac{1}{M - 1} \sum_{m=1}^{M} \left(C^{(m)} - \bar C\right)^2

and the returned estimate for the variance of the mean is s^2 / M. The first describes dispersion between members. Interpreting the second as Monte Carlo precision assumes comparable components and independent realizations with a common mean and a common finite covariance. Opposite perturbations in a complementary pair are dependent; the two signs do not provide independent realizations for this interpretation.

The function does not establish these statistical assumptions or physical correspondence between equal mode indices. Dispersion under perturbations of a fixed record does not quantify all uncertainty in the physical signal, and increasing the number of members does not remove decomposition bias. Attributes of realizations other than dim do not reach the outputs.

Value

A list with two matrices, samples by modes:

variance	The sample variance s^2, in squared units of the signal.
meanVariance	The estimate s^2 / M, subject to the assumptions in Details.

See Also

decomposeEEMD

Examples

# Two realizations of four samples: the first has two modes, the second
# one, so its second mode is filled with zeros.
Realizations <- array(c(2, 4, 6, 8, 1, 1, 1, 1,
                        4, 6, 8, 10, 0, 0, 0, 0), dim = c(4, 2, 2))
measureDispersion(Realizations)

xemd documentation built on Nov. 9, 2026, 1:09 a.m.