Levy-flight tail exponent on consecutive-incident steps — morie_tps_levy_flight

Computes the Hill maximum-likelihood estimator of the upper-tail Pareto exponent $\alpha$ of the step-length distribution between chronologically consecutive incidents, following Brockmann, Hufnagel & Geisel (2006). For a power-law tail $p(\ell) \propto \ell^{-\alpha}$ on $\ell \ge \ell_{\min}$ the Hill MLE is $$\hat\alpha = 1 + n / \sum_i \log(\ell_i / \ell_{\min}).$$ Standard error is obtained by 200 nonparametric bootstrap resamples.

Usage

morie_tps_levy_flight_alpha(
  category = "Assault",
  sample_rows = 30000L,
  lmin_km = 0.5,
  save_fig = TRUE
)

Arguments

category: TPS category name.
sample_rows: Maximum rows to load.
lmin_km: Lower tail cutoff in km.
save_fig: Whether to emit a log-log empirical-vs-fit PNG.

Value

A morie_rich_result with $\hat\alpha$, bootstrap SE, sample-size diagnostics, and a Lévy-regime interpretation.

References

Brockmann D, Hufnagel L, Geisel T (2006). The scaling laws of human travel. Nature 439: 462-465.

Examples

if (FALSE) { # \dontrun{
  rr <- morie_tps_levy_flight_alpha("Assault", save_fig = FALSE)
  print(rr$summary_lines$alpha)
} # }