foapy.characteristics.ma
The package provides a comprehensive set of vector characteristics for measuring the properties of a cogeneric order.
The table below summarizes vector representation of the characteristics that depend only on intervals:
| Linear scale | Logarifmic scale | ||
|---|---|---|---|
| Arithmetic Mean | \(\left[ \Delta_{a_j} \right]_{1 \le j \le m} = \left[ \frac{1}{n_j} * \sum_{i=1}^{n_j} \Delta_{ij} \right]_{1 \le j \le m}\) | ||
| Geometric Mean | \(\left[ \Delta_{g_j} \right]_{1 \le j \le m} = \left[ \left( \prod_{i=1}^{n_j} \Delta_{ij} \right)^{1/n_j} \right]_{1 \le j \le m}\) | \(\left[ g_j \right]_{1 \le j \le m} = \left[ \frac{1}{n_j} * \sum_{i=1}^{n_j} \log_2 \Delta_{ij} \right]_{1 \le j \le m}\) | Average Remoteness |
| Volume | \(\left[ V_j \right]_{1 \le j \le m} = \left[ \prod_{i=1}^{n_j} \Delta_{ij} \right]_{1 \le j \le m}\) | \(\left[ G_j \right]_{1 \le j \le m} = \left[ \sum_{i=1}^{n_j} \log_2 \Delta_{ij} \right]_{1 \le j \le m}\) | Depth |
The table below summarizes the advanced characteristics of cogeneric intervals:
| Characteristics | |
|---|---|
| Identifying Information | \(\left[ H_j \right]_{1 \le j \le m} = \left[ \log_2 { \left(\frac{1}{n_j} * \sum_{i=1}^{n_j} \Delta_{ij} \right) } \right]_{1 \le j \le m}\) |
| Periodicity | \(\left[ \tau_j \right]_{1 \le j \le m} = \left[ \left( \prod_{i=1}^{n_j} \Delta_{ij} \right)^{1/n_j} * \frac{ n_j }{ \sum_{i=1}^{n_j} \Delta_{ij} } \right]_{1 \le j \le m}\) |
| Uniformity | \(\left[ u_j \right]_{1 \le j \le m} = \left[ \log_2 { \left(\frac{1}{n_j} * \sum_{i=1}^{n_j} \Delta_{ij} \right) } - \frac{1}{n_j} * \sum_{i=1}^{n_j} \log_2 \Delta_{ij} \right]_{1 \le j \le m}\) |