Table 2 Formula and descriptions for non-sequential summary statistics \(t_k(w) = \sum _j Y_{jk}\) formed from different choices of \(Y_{jk}\)
From: Kernel density estimation of conditional distributions to detect responses in satellite tag data
Order-sensitivity | k | Description of \(t_k(w) = \sum _j Y_{jk}\) | \(Y_{jk}\) |
|---|---|---|---|
None | 1 | Time on or near surface | \({\varvec{1}} \left\{ z_j \in {\mathcal {S}} \right\}\) |
2 | Average depth | \(z_j / W\) | |
3 | Time in deep dives | \(\ell (z_j)\) | |
Pairwise | 4 | Time spent ascending | \({\varvec{1}} \left\{ d_j < 0 \right\}\) |
5 | Time spent descending | \({\varvec{1}} \left\{ d_j > 0 \right\}\) | |
6 | Time spent without vertical movement | \({\varvec{1}} \left\{ d_j = 0 \right\}\) | |
7 | Total vertical distance traveled | \(\vert d_j \vert\) | |
8 | Total ascent distance | \(\vert d_j \vert {\varvec{1}} \left\{ d_j < 0 \right\}\) | |
9 | Total descent distance | \(\vert d_j \vert {\varvec{1}} \left\{ d_j > 0 \right\}\) | |
10 | Total vertical direction changes | \({\varvec{1}} \left\{ \text{ H }(d_{j+1}) \ne \text{ H }(d_j) \right\}\) |