Variance V


This aggregation_operator calculates the variance for all elements in the group.It is implemented as follow:

Where:

Xiis the index value for the ith amino acid.
Xis the mean of the indices values.
nis the number of amino acid.

Variability Coefficient CV


This aggregation_operator calculates de variability coefficient for all elements in the group.

Where:

sis the variance for the group.
Xis the mean of the indices values.

Standard Desviation DE


This aggregation_operator calculate the standard desviation for the group.It is implemented as follow:

Where:

Xiis the index value for each amino acid.
Xis the mean of the indices values.
nis the number of amino acid in the group.

Kurtosis K


Represents the area traced by the center of a rolling sphere over the residue surface, this index takes value cero when the amino acid is fully buried.

Where:

Mj
s4is the standard deviation raised to the fourth power.
nis the number of amino acid in the group.

Skewness S


Skewness (this term was first used by Pearson, 1895) measures the deviation of the distribution from symmetry. If the skewness is clearly different from 0, then that distribution is asymmetrical, while normal distributions are perfectly symmetrical.

Where:

M3
s3is the standard desviation (sigma) raised to the third power. The standard deviation (s) is the root of the variance (S).
nis the number of amino acid in the group

Range RA


This aggregation_operator calculate the range value.It is implemented as follow:

Where:

Xmaxis the maximum index value in the group.
Xminis the minimum index value in the group

Minimum Value MN


This aggregation_operator calculate the minimum index value contained in the group.

Maximum Value MX


This aggregation_operator calculate the maximum index value contained in the group.

Quartile Q1


This aggregation_operator calculates the element located in the 25% of the sorted group.

Quartile Q2


This aggregation_operator calculates the element located in the 50% in the sorted group.

Quartile Q3


This aggregation_operator calculates the element located in the 75% in the sorted group.

I50


This aggregation_operator calculate the I50 value for the group. It is implemented as follow:

Where:

P75is the quartile Q3.
P25is the quartile Q1.