Table 2 Aggregation measures.

Variance(ag1)

\(var(p)=\frac{\sigma _p}{\mu _p}\)

Arithmetic Mean(ag2)

\(\mu _p=\frac{1}{R}\sum _{q=1}^{R}p_q\)

Skewness(ag3)

\(\gamma _1=\displaystyle {\frac{\sum _{q=1}^{R}( p-\overline{p})^3/R}{(\sigma (p))^3}}\)

Minimum

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Median(ag4)

\(M_{p} ={\left\{ \begin{array}{ll}p_{R+1/2} & if R is odd\\ 1/2(p_{R/2}+p_{R+2/2}) & otherwise\end{array}\right. }\)

Quartile1(25\(\%\))(ag5)

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Theli Index (ag6)

\(I_{Theli}(p)={\frac{1}{R}}\sum _{q=1}^{R}(\frac{p_q}{\mu _s}*\ln (\frac{p_q}{\mu _s}))\)

Standard Deviation (ag7)

\(\sigma _p= \sqrt{\frac{1}{R}\sum _{q=1}^{R}(p_q-\mu _q)^2}\)

Quartile3(75\(\%\)) (ag8)

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Generalized Entropy (ag9)

\(GE_p =-\frac{1}{R\alpha (1-\alpha )}\sum _{q=1}^{R}[({\frac{p_q}{\mu _p}})^\alpha -1],\alpha =0.5\)

Maximum (ag10)

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Gini Index(ag11)

\(I_{Gini}(p)=\frac{2}{R\sum _{p}}[{\sum _{q=1}^{R}}(p_q*q)-(R+1)\sum _{p}]\)

kurtosis (ag12)

\(\gamma _2=\displaystyle {\frac{\sum _{q=1}^{R}( p-\overline{p})^4/R}{(\sigma (p))^4}}\)

Hoover Index

\(I_{Hoover}(p)= {\frac{1}{2}}\sum _{q=1}^{R}|\frac{p_q}{\sum _{p}}-\frac{1}{R}|\)

Atkinson Index(ag13)

\(I_{Atkinson}(p)=1-{\frac{1}{\mu _p}}({\frac{1}{R}}\sum _{q=1}^{R}\sqrt{p_q})^2\)

Shannon Entropy

\(E_p=-\frac{1}{R}\sum _{p=1}^{R}[\frac{freq(p_q)}{R}*\ln \frac{freq(p_q)}{R}]\)