Skewness

Skewness is a statistic that is used to measure the symmetry of the distribution for a set of data. The skewness of an analysis domain is calculated as follows:

Skewness = K3 / ESD 3

where:

K3 = [n · Σi (Ei - En)3] / [(n-1)·(n-2)] if n ≥ 3;
K3 = 0 if n < 3

summation is over all samples i in the region, or interval, or analysis domain,

n is the number of samples included in the summation.

Ei is the linear Sv of sample i (m2/m3) - set to 0 for any sample where Ei < mSv or Ei > MSv,

En is the observed Mean Energy of the region in linear units (m2/m3) = 10Sv/10

mSv is the minimum integration threshold (dB re 1 m-1) at time of processing.

MSv is the maximum integration threshold (dB re 1 m-1) at time of processing.

ESD Standard_deviation (Standard Deviation of the Energy)

For samples with a linear data type, Eii is the sample value, Enis the sample mean of the analysis domain.

For samples with a dB data type (TS, Power dB or Unspecified dB): Eii is the linear equivalent of the sample value and Enis the linear equivalent of the sample mean of the analysis domain. See also: Note for undefined behavior.

All symbols are as defined in the nomenclature developed for SHAPES algorithms.

n	is the number of samples included in the summation.
Ei	is the linear Sv of sample i (m2/m3) - set to 0 for any sample where Ei < mSv or Ei > MSv,
En	is the observed Mean Energy of the region in linear units (m2/m3) = 10Sv/10
mSv	is the minimum integration threshold (dB re 1 m-1) at time of processing.
MSv	is the maximum integration threshold (dB re 1 m-1) at time of processing.
ESD	Standard_deviation (Standard Deviation of the Energy)