f_distribution

Note Master 25-07-2026

The share of the stay's time spent near the candidate. It counts the GPS points within R_buffer of the candidate, weighted by time:

\[f_\text{distribution}(E_k, C_i) = \frac{\sum_{p \in C_i} W_p \cdot \mathbf{1}\{d(p, E_k) \leq R_\text{buffer}\}}{\sum_{p \in C_i} W_p}\]

\(\mathbf{1}\{\dots\}\) is 1 when point \(p\) is close enough to the candidate and 0 otherwise. \(W_p\) is the time weight of point \(p\) (following Wu et al., 2026). Phones do not record points at even time steps, so each point gets a weight equal to the time it stands for. Points in the middle get \(W_p = (t_{p+1} - t_{p-1})/2\), half the time between the point before and the point after. The first and last points get:

\[W_1 = \frac{t_1 + t_2}{2}, \qquad W_n = 1 - \frac{t_{n-1} + t_n}{2}\]

In the models: this score was significant from the very first model (Model 1: base), and it is the strongest open-space term in the Final model. Its product with share_type is the only combined term that the final model kept (Interaction term screen (α = 1)).

Part of Framework overview.

Linked from Assignment framework · Candidate selection · Framework overview · Model 1: base · f_temporal