generate_vonmises_grid: Generate a Calibration Grid for the von Mises Concentration...

In bpDir: Boxplots for Directional Data

Generate a Calibration Grid for the von Mises Concentration Parameter

Description

Generates a calibration grid relating robust measures of circular dispersion to the circular standard deviation (CSD) and the concentration parameter (\kappa) of a von Mises distribution.

The grid is used by the estimation procedure to convert an observed robust circular dispersion statistic into an estimate of CSD through monotone spline interpolation, and subsequently into an estimate of the von Mises concentration parameter.

Usage

generate_vonmises_grid(
  rho_seq = seq(0.01, 0.99, by = 0.002)
)

Arguments

rho_seq

A numeric vector of values of the mean resultant length \rho for which the calibration grid is generated. Values must lie strictly between 0 and 1. The default sequence ranges from 0.01 to 0.99 in increments of 0.002.

Details

The calibration grid is constructed by evaluating the dispersion statistics over a sequence of von Mises distributions with different values of the concentration parameter \kappa.

A precomputed calibration grid can be supplied to the estimation function through its results_grid argument, avoiding the need to regenerate the grid for every estimation.

Value

A data frame with the following columns:

kappa

Values of the von Mises concentration parameter, calculated by applying circular::A1inv to the corresponding values of \rho.

rho

Values of the mean resultant length.

CSD

The circular standard deviation, calculated as 2(1-\rho).

CMAD

Calibration values obtained using the 0.75 quantile of the centred von Mises distribution, for the CMAD-based estimation procedure.

CLMS

Calibration values obtained using the 0.75 quantile of the centred von Mises distribution, for the CLMS-based estimation procedure.

CLTS

Calibration values computed using the internal procedure for the von Mises distribution, for the CLTS-based estimation procedure.

See Also

CircularMAD CircularLMS CircularLTS

Examples

# Generate a custom calibration grid
custom_grid <- generate_vonmises_grid(
  rho_seq = seq(0.05, 0.95, length.out = 50)
)

head(custom_grid)

bpDir documentation built on Nov. 9, 2026, 9:07 a.m.