Fit a wrapped Cauchy distribution to per-group heading data

Estimates the mean direction \(\mu\) and concentration \(\rho\) of a wrapped Cauchy distribution via maximum likelihood. The wrapped Cauchy has heavier tails than the von Mises and is more appropriate for data with outliers, weak or noisy directionality, or when a von Mises fit looks visually poor on a rose diagram.

Usage

wrappedcauchy_fit(hd, group_col = NULL, angle_col = "heading", axial = FALSE)

Arguments

hd

Data frame containing headings in radians.

group_col

Column(s) to group by. NULL fits a single model.

angle_col

Name of the heading column. Default "heading".

axial

Logical; when `TRUE`, fit an axial (bidirectional, mod-pi) wrapped Cauchy via the doubled-angle method: `mu`/`mu_deg` are the mean **axis** in [0, pi) and `rho` is the concentration about that axis (estimated in the doubled-angle frame). Default `FALSE` (directional).

Value

Data frame with columns group_col (if supplied), mu (MLE mean direction, radians), mu_deg (degrees), rho (concentration, 0–1), convergence (0 = converged, 1 = not converged; NA when the fit could not be attempted), n.

Details

\(\rho = 0\) is a uniform distribution (no preferred direction); \(\rho = 1\) is a point mass (perfect concentration). Unlike von Mises \(\kappa\), the wrapped Cauchy \(\rho\) is bounded to \([0, 1)\).

Standard errors are not computed by mle.wrappedcauchy; check the convergence flag (0 = the fixed-point MLE iteration converged; 1 = it did not, so treat that row's estimates with caution). For uncertainty estimation use vonmises_fit with the same data and compare model fits visually via add_vonmises_density and add_wrappedcauchy_density.

See also

vonmises_fit, add_wrappedcauchy_density