Table 3 Definition of thirty-six statistical indicators [25]

F ₁

Maximum value

The maximum value in x(n), i.e., max(x(n))

F ₂

Minimum value

The minimum value in x(n), i.e., min(x(n))

F ₃

Mean

\(\overline{x} = \frac{1}{N}\sum\limits_{n = 1}^{N} {x(n)}\)

F ₄

Peak to peak

max(x(n))−min(x(n))

F ₅

Harmonic mean

\(\frac{N}{{\sum\limits_{n = 1}^{N} {\frac{1}{x(n)}} }}\)

F ₆

Trimmed mean

Mean excluding outliers

F ₇

Variance

\(\frac{1}{N}\sum\limits_{n = 1}^{N} {\left( {x(n) - \bar{x}} \right)^{2} }\)

F ₈

Standard deviation

\(\sqrt {\frac{1}{N}\sum\limits_{n = 1}^{N} {\left( {x(n) - \bar{x}} \right)^{2} } }\)

F ₉

Mean absolute deviation

\(\frac{1}{N}\sum\limits_{n = 1}^{N} {\left| {x(n) - \bar{x}} \right|}\)

F ₁₀

Median absolute deviation

\(\frac{1}{N}\sum\limits_{n = 1}^{N} {\left| {x(n) - x_{\text{median}} } \right|}\)

F ₁₁

Interquartile range

The 1st quartile subtracted from the 3rd quartile

F ₁₂

Peak2RMS

\(\frac{{\hbox{max} (\left| {x(n)} \right|)}}{{\sqrt {\frac{1}{N}\sum\limits_{n = 1}^{N} {x(n)^{2} } } }}\)

F ₁₃

Skewness

\(\frac{{\frac{1}{N}\sum\limits_{n = 1}^{N} {\left( {x(n) - \bar{x}} \right)^{3} } }}{{\left( {\sqrt {\frac{1}{N}\sum\limits_{n = 1}^{N} {\left( {x(n) - \bar{x}} \right)^{2} } } } \right)^{3} }}\)

F ₁₄

Kurtosis

\(\frac{{\frac{1}{N}\sum\limits_{n = 1}^{N} {\left( {x(n) - \bar{x}} \right)^{4} } }}{{\left( {\frac{1}{N}\sum\limits_{n = 1}^{N} {\left( {x(n) - \bar{x}} \right)^{2} } } \right)^{2} }}\)

F ₁₅

Shape factor

\(\frac{{\sqrt {\frac{1}{N}\sum\limits_{n = 1}^{N} {x(n)^{2} } } }}{{\frac{1}{N}\sum\limits_{n = 1}^{N} {\left| {x(n)} \right|} }}\)

F ₁₆

Crest factor

\(\frac{\hbox{max} (x(n))}{{\sqrt {\frac{1}{N}\sum\limits_{n = 1}^{N} {x(n)^{2} } } }}\)

F ₁₇

Clearance factor

\(\frac{\hbox{max} (x(n))}{{\frac{1}{N}\sum\limits_{n = 1}^{N} {x(n)^{2} } }}\)

F ₁₈

Impulse factor

\(\frac{\hbox{max} (x(n))}{{\frac{1}{N}\sum\limits_{n = 1}^{N} {\left| {x(n)} \right|} }}\)

F ₁₉

Third order central moment

\(\frac{1}{N}\sum\limits_{n = 1}^{N} {\left( {x(n) - \bar{x}} \right)^{3} }\)

F ₂₀

Fourth order central moment

\(\frac{1}{N}\sum\limits_{n = 1}^{N} {\left( {x(n) - \bar{x}} \right)^{ 4} }\)

F ₂₁

Root mean square

\(\sqrt {\frac{1}{N}\sum\limits_{n = 1}^{N} {x(n)^{2} } }\)

F ₂₂

Energy operator

\(\frac{{\frac{1}{N}\sum\limits_{n = 1}^{N} {\left( {\Delta x(n) - \Delta \overline{x} } \right)^{4} } }}{{\left( {\frac{1}{N}\sum\limits_{n = 1}^{N} {\left( {\Delta x(n) - \Delta \overline{x} } \right)^{2} } } \right)^{2} }}\)

F ₂₃

Mean frequency

\(\frac{1}{K}\sum\limits_{k = 1}^{K} {X(k)}\)

F ₂₄

Frequency center

\(\frac{{\sum\limits_{k = 1}^{K} {\left( {f(k) \times X(k)} \right)} }}{{\sum\limits_{k = 1}^{K} {X(k)} }}\)

F ₂₅

Root mean square frequency

\(\sqrt {\frac{{\sum\limits_{k = 1}^{K} {\left( {f(k)^{2} \times X(k)} \right)} }}{{\sum\limits_{k = 1}^{K} {X(k)} }}}\)

F ₂₆

Standard deviation frequency

\(\sqrt {\frac{{\sum\limits_{k = 1}^{K} {\left( {\left( {f(k) - F_{28} } \right)^{2} \times X(k)} \right)} }}{{\sum\limits_{k = 1}^{K} {X(k)} }}}\)

F ₂₇

NA4

\(\frac{{\frac{1}{N}\sum\limits_{n = 1}^{N} {\left( {r(n) - \overline{r} } \right)^{4} } }}{{\left( {\frac{1}{M}\sum\limits_{m = 1}^{M} {\left( {\frac{1}{N}\sum\limits_{n = 1}^{N} {\left( {r_{m} (n) - \overline{r}_{m} } \right)^{2} } } \right)} } \right)^{2} }}\)

F ₂₈

NA4^*

\(\frac{{\frac{1}{N}\sum\limits_{n = 1}^{N} {\left( {r(n) - \overline{r} } \right)^{4} } }}{{\left( {\frac{1}{{M^{'} }}\sum\limits_{m = 1}^{{M^{'} }} {\frac{1}{N}\sum\limits_{n = 1}^{N} {\left( {r_{m} (n) - \overline{r}_{m} } \right)^{2} } } } \right)^{2} }}\)

F ₂₉

FM4

\(\frac{{\frac{1}{N}\sum\limits_{n = 1}^{N} {\left( {d(n) - \overline{d} } \right)^{4} } }}{{\left( {\frac{1}{N}\sum\limits_{n = 1}^{N} {\left( {d(n) - \overline{d} } \right)^{2} } } \right)^{2} }}\)

F ₃₀

FM4^*

\(\frac{{\frac{1}{N}\sum\limits_{n = 1}^{N} {\left( {d(n) - \overline{d} } \right)^{4} } }}{{\left( {\frac{1}{{M^{'} }}\sum\limits_{m = 1}^{{M^{'} }} {\left( {\frac{1}{N}\sum\limits_{n = 1}^{N} {\left( {d_{m} (n) - \overline{d}_{m} } \right)^{2} } } \right)} } \right)^{2} }}\)

F ₃₁

M6A

\(\frac{{\frac{1}{N}\sum\limits_{n = 1}^{N} {\left( {d(n) - \overline{d} } \right)^{6} } }}{{\left( {\frac{1}{N}\sum\limits_{n = 1}^{N} {\left( {d(n) - \overline{d} } \right)^{2} } } \right)^{3} }}\)

F ₃₂

M6A^*

\(\frac{{\frac{1}{N}\sum\limits_{n = 1}^{N} {\left( {d(n) - \overline{d} } \right)^{6} } }}{{\left( {\frac{1}{{M^{'} }}\sum\limits_{m = 1}^{{M^{'} }} {\left( {\frac{1}{N}\sum\limits_{n = 1}^{N} {\left( {d_{m} (n) - \overline{d}_{m} } \right)^{2} } } \right)} } \right)^{3} }}\)

F ₃₃

M8A

\(\frac{{\frac{1}{N}\sum\limits_{n = 1}^{N} {\left( {d(n) - \overline{d} } \right)^{8} } }}{{\left( {\frac{1}{N}\sum\limits_{n = 1}^{N} {\left( {d(n) - \overline{d} } \right)^{2} } } \right)^{4} }}\)

F ₃₄

M8A^*

\(\frac{{\frac{1}{N}\sum\limits_{n = 1}^{N} {\left( {d(n) - \overline{d} } \right)^{8} } }}{{\left( {\frac{1}{{M^{'} }}\sum\limits_{m = 1}^{{M^{'} }} {\left( {\frac{1}{N}\sum\limits_{n = 1}^{N} {\left( {d_{m} (n) - \overline{d}_{m} } \right)^{2} } } \right)} } \right)^{4} }}\)

F ₃₅

NB4

\(\frac{{\frac{1}{N}\sum\limits_{n = 1}^{N} {\left( {e(n) - \overline{e} } \right)^{4} } }}{{\left( {\frac{1}{M}\sum\limits_{m = 1}^{M} {\left( {\frac{1}{N}\sum\limits_{n = 1}^{N} {\left( {e_{m} (n) - \overline{e}_{m} } \right)^{2} } } \right)} } \right)^{2} }}\)

F ₃₆

NB4^*

\(\frac{{\frac{1}{N}\sum\limits_{n = 1}^{N} {\left( {e(n) - \overline{e} } \right)^{4} } }}{{\left( {\frac{1}{{M^{'} }}\sum\limits_{m = 1}^{{M^{'} }} {\left( {\frac{1}{N}\sum\limits_{n = 1}^{N} {\left( {e_{m} (n) - \overline{e}_{m} } \right)^{2} } } \right)} } \right)^{2} }}\)