Parameter

Microscopic/ macroscopic

Formula

Reference

Mean, $\overline{{\epsilon }_s}$

Macroscopic

$\overline{{\epsilon }_s}=\frac{1}{N}{\displaystyle \sum _{i=1}^N{\epsilon }_s\left(i\right)}$

[1] [7] [8] [12] [16]

Standard Deviation, $\sigma \left({\epsilon }_s\right)$

Microscopic

$\sigma \left({\epsilon }_s\right)=\sqrt{\frac{1}{N-1}{\displaystyle \sum _{i=1}^N{\left({\epsilon }_s\left(i\right)-\overline{{\epsilon }_s}\right)}^2}}$

[8] [22] [23]

Skewness, $S_k$

Microscopic

$S_k=\frac{1}{N\sigma {\left({\epsilon }_S\right)}^3}{\displaystyle \sum _{i=1}^N{\left({\epsilon }_S\left(i\right)-\overline{{\epsilon }_S}\right)}^3}$

[7] [8] [23]

Kurtosis, $K_u$

Microscopic

$K_u=\frac{1}{N\sigma {\left({\epsilon }_S\right)}^4}{\displaystyle \sum _{i=1}^N{\left({\epsilon }_S\left(i\right)-\overline{{\epsilon }_S}\right)}^4}$

[8] [23]

Intermittent Index, $\gamma$

Macroscopic

$\gamma =\frac{\sigma \left({\epsilon }_s\right)}{\sigma {\left({\epsilon }_s\right)}_{\max }}=\frac{\sigma \left({\epsilon }_s\right)}{\sqrt{\overline{\overline{{\epsilon }_s}\left(1-\overline{{\epsilon }_s}-{\epsilon }_{s,mf}\right)}}}$

[7] [22]

Average Absolute Deviation (AAD)

Microscopic

$AAD=\frac{1}{N}{\displaystyle \sum _{i=1}^N\left(\left|{\epsilon }_s\left(i\right)-\overline{{\epsilon }_s}\right|\right)}$

[18] [23]

Radial Non-Uniformity Index (RNI)

Macroscopic

$RNI\left({\epsilon }_s\right)=\frac{\sigma \left({\epsilon }_s\right)}{\sigma {\left({\epsilon }_s\right)}_{\max }}=\frac{\sigma \left({\epsilon }_s\right)}{\sqrt{\overline{{\epsilon }_s}\left({\epsilon }_{s,mf}-\overline{{\epsilon }_s}\right)}}$

[16] [21]

Probability Density Function (PDF)

Microscopic

$f\left(x\right)=\mathrm{Pr}\left[{\epsilon }_s=x\right]$

[1] [7] [12]

Coefficient of Variation, CV

Macroscopic

$CV=\frac{\sigma \left({\epsilon }_s\right)}{\overline{{\epsilon }_s}}$

[18] [23]