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")

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".

Value

Data frame with columns group_col (if supplied), mu (MLE mean direction, radians), mu_deg (degrees), rho (concentration, 0–1), convergence (0 = converged), 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 convergence is the optim return code (0 = fully converged; 1 = iteration limit reached but estimates are typically still reliable). 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