foapy.characteristics

The package provides a comprehensive set of characteristics for measuring the properties of given order.

The table below summarizes the available characteristics that depend only on intervals:

Linear scale			Logarifmic scale
Arithmetic Mean	\(\Delta_a = \frac{1}{n} * \sum_{i=1}^{n} \Delta_{i}\)
Geometric Mean	\(\Delta_g=\sqrt[n]{\prod_{i=1}^{n} \Delta_{i}}\)		\(g = \frac{1}{n} * \sum_{i=1}^{n} \log_2 \Delta_{i}\)	Average Remoteness
Volume	\(V=\prod_{i=1}^{n} \Delta_{i}\)		\(G=\sum_{i=1}^{n} \log_2 \Delta_{i}\)	Depth

The table below summarizes the available characteristics that depend on cogeneric intervals ( grouped by element of the alphabet):

Characteristics
Descriptive Information	\(D=\prod_{j=1}^{m}{\left(\sum_{i=1}^{n_j}{\frac{\Delta_{ij}}{n_j}}\right)^{\frac{n_j}{n}}}\)
Identifying Information	\(H=\frac {1} {n} * \sum_{j=1}^{m}{(n_j * \log_2 \sum_{i=1}^{n_j} \frac{\Delta_{ij}}{n_j})}\)
Regularity	\(r= \sqrt[n]{\prod_{j=1}^{m} \frac{\prod_{j=1}^{n_j} \Delta_{ij}}{{\left(\frac{1}{n_j}\sum_{i=1}^{n_j}{\Delta_{ij}}\right)^{n_j}}}}\)
Uniformity	\(u = \frac {1} {n} * \sum_{j=1}^{m}{\log_2 \frac{ (\sum_{i=1}^{n_j} \frac{\Delta_{ij}}{n_j})^{n_j} } { \prod_{i=1}^{n_j} \Delta_{ij}}}\)

ma subpackage provides characteristics for cogeneric intervals ( grouped by element).