Package 'bpDir' reference manual

Title:	Boxplots for Directional Data
Description:	Functions for drawing boxplots for data on (the boundary of) a unit circle (i.e., circular and axial data), from Buttarazzi D., Pandolfo G., Porzio G.C. (2018) <doi:10.1111/biom.12889>. The package allows producing also circular violin plots, and includes methods to calculate robust measures of dispersion for circular data.
Authors:	Davide Buttarazzi [aut, cre]
Maintainer:	Davide Buttarazzi <[email protected]>
License:	GPL-2
Version:	0.2.6
Built:	2026-11-09 19:10:05 UTC
Source:	https://github.com/cran/bpDir

AxialBoxplot

Description

Draw a boxplot for axial data

Usage

AxialBoxplot(A, template = "degrees", place = "none", marg =
                   "large", stack = FALSE, H = FALSE, shrink = 1.5, units
                   = "degrees", constant = "optimal", concentration = NULL, mirror = TRUE)
AxialBoxplot(A, template = "degrees", place = "none", marg =
                   "large", stack = FALSE, H = FALSE, shrink = 1.5, units
                   = "degrees", constant = "optimal", concentration = NULL, mirror = TRUE)

Arguments

A

numeric; a vector of class circular in units=c("degrees", "radians")

template

character; graphical parameter to set the template to be used in the plot. Options are "degrees"(default), "radians" and "geographics". If NULL, a generic template can be defined, with angles displayed according to the graphical parameter place.

place

character; graphical parameter. Active only when template = NULL to add an additional generic template either "outside" or "inside" the circle.
If place = "none"(default), no additional template is plotted.

marg

character; graphical parameter to set the plot region to either "large"(default) or "small", expressed in number of lines of text.

stack

If TRUE and H=FALSE, then far out values are stacked on the circumference.

H

logical; graphical parameter to specify if observations between the hinges and the whiskers are plotted. Default is FALSE.

shrink

numeric; graphical parameter to control the size of the plotted circle. Default is 1.5. Larger values shrink the circle, while smaller values enlarge the circle.

units

character; graphical parameter to select the unit of measure to be displayed on the axes when template = NULL and place=c("inside","outside"). Options are "degrees"(default) or "radians".

constant

numeric; the boxplot multiplying factor (or "constant") that determines how far the fences extend out from the box. When "optimal"(default), it ensures the probability that an observation falls outside the fences (i.e., it will be a far out value) is 0,7% under a von Mises distribution (see Web Appendix A in Buttarazzi et al., 2018).

concentration

numeric; if constant = "optimal", this argument can be used to specify the concentration parameter to be used to estimate the boxplot multiplying factor.

mirror

If TRUE, then a second axial boxplot will be plotted on the opposite semi-circle.

Details

The arguments stack, shrink are parameters passed to plot.circular.

Value

farout

a vector of class circular in radians, containing the values of the points lying outside the whiskers.

constant

the value of the constant used to draw the boxplot.

Author(s)

Davide Buttarazzi

References

Buttarazzi D., Pandolfo G., Porzio G.C. (2018). A boxplot for circular data, Biometrics.

Examples

set.seed(1)
#install.packages("circular")
require(circular)
#install.packages("plotrix")
require(plotrix)
theta <- circular::rvonmises(100, circular(pi/2), 3, control.circular=list(units="radians"))
axialTheta <- circular(theta, modulo = "pi")
AxialBoxplot(axialTheta, template = "radians", mirror = FALSE)
set.seed(1)
#install.packages("circular")
require(circular)
#install.packages("plotrix")
require(plotrix)
theta <- circular::rvonmises(100, circular(pi/2), 3, control.circular=list(units="radians"))
axialTheta <- circular(theta, modulo = "pi")
AxialBoxplot(axialTheta, template = "radians", mirror = FALSE)

Circular Box-and-Wisker Plot

Description

The CircularBoxplot function produces a box-and-whisker-plot for circular data.

Usage

CircularBoxplot ( A, template="degrees", place="none", units="degrees", marg=
                   "large", shrink = 1.5,  H=FALSE, stack=FALSE, constant=
                   "optimal", concentration= NULL)

CircularBoxplot ( A, template="degrees", place="none", units="degrees", marg=
                   "large", shrink = 1.5,  H=FALSE, stack=FALSE, constant=
                   "optimal", concentration= NULL)

Arguments

A

numeric; a vector of class circular in units=c("degrees", "radians")

template

place

units

character; graphical parameter to select the unit of measure to be displayed on the axes when template = NULL and place=c("inside","outside"). Options are "degrees"(default) or "radians".

marg

character; graphical parameter to set the plot region to either "large"(default) or "small", expressed in number of lines of text.

shrink

numeric; graphical parameter to control the size of the plotted circle. Default is 1.5. Larger values shrink the circle, while smaller values enlarge the circle.

H

logical; graphical parameter to specify if observations between the hinges and the whiskers are plotted. Default is FALSE.

stack

If TRUE and H=FALSE, then far out values are stacked on the circumference.

constant

concentration

numeric; if constant = "optimal", this argument can be used to specify the concentration parameter to be used to estimate the boxplot multiplying factor.

Details

The arguments stack, shrink are parameters passed to plot.circular.

Value

farout

a vector of class circular in radians, containing the values of the points lying outside the whiskers.

statistics

a dataframe of summary statistics in degrees: circular median, hinges and whiskers.

constant

the value of the constant used to draw the boxplot.

Author(s)

Davide Buttarazzi

References

Buttarazzi D., Pandolfo G., Porzio G.C. (2018). A boxplot for circular data, Biometrics.

Examples

# Circular Boxplot on Vanishing directions of homing pigeons
#install.packages("circular")
#install.packages("plotrix")
require(circular)
require(plotrix)
#help(fisherB12c)
data(fisherB12c)
CircularBoxplot(fisherB12c, template="geographics")
# Circular Boxplot on Vanishing directions of homing pigeons
#install.packages("circular")
#install.packages("plotrix")
require(circular)
require(plotrix)
#help(fisherB12c)
data(fisherB12c)
CircularBoxplot(fisherB12c, template="geographics")

Compute the robust measure of circular spread: the Circular Least Median Spread (CLMS)

Description

Compute the Circular Least Median Spread (Demni et al, 2026)

Usage

CircularLMS(X)
CircularLMS(X)

Arguments

X

numeric; a vector of class circular in units=c("radians")

Value

Circular Least Median Spread (CLMS)

Author(s)

Davide Buttarazzi, Houyem Demni

References

Demni et al. (2026), Robust measures of dispersion for circular data with an anomaly detection rule. Under review.

Examples

#install.packages("circular")
require(circular)
data1 <- rvonmises(50, circular(pi/2), 5)
CircularLMS(data1)
#install.packages("circular")
require(circular)
data1 <- rvonmises(50, circular(pi/2), 5)
CircularLMS(data1)

Compute the robust measure of circular spread: the Circular Least Trimmed Standard deviation (CLTS)

Description

Compute the Circular Least Trimmed Standard deviation (Demni et al, 2026)

Usage

CircularLTS(X)
CircularLTS(X)

Arguments

X

numeric; a vector of class circular in units=c("radians")

Value

Circular Least Trimmed Standard deviation (CLTS)

Author(s)

Davide Buttarazzi, Houyem Demni

References

Demni et al. (2026), Robust measures of dispersion for circular data with an anomaly detection rule. Under review.

Examples

#install.packages("circular")
require(circular)
data1 <- rvonmises(50, circular(pi/2), 5)
CircularLTS(data1)
#install.packages("circular")
require(circular)
data1 <- rvonmises(50, circular(pi/2), 5)
CircularLTS(data1)

Compute the robust measure of circular spread: the Circular Median Absolute Deviation (CMAD)

Description

Compute the Circular Median Absolute Deviation (Demni et al, 2026)

Usage

CircularMAD(X, h = FALSE)
CircularMAD(X, h = FALSE)

Arguments

X

numeric; a vector of class circular in units=c("radians")

h

logical; optionally produce histogram of the distances between the median and X, set to FALSE by default.

Value

Circular Median Absolute Deviation (CMAD)

Author(s)

Davide Buttarazzi, Houyem Demni

References

Demni et al. (2026), Robust measures of dispersion for circular data with an anomaly detection rule. Under review.

Examples

#install.packages("circular")
require(circular)
data1 <- rvonmises(50, circular(pi/2), 5)
CircularMAD(data1)
#install.packages("circular")
require(circular)
data1 <- rvonmises(50, circular(pi/2), 5)
CircularMAD(data1)

Circular Tukey Depth

Description

Empirical depth ranking based on Tukey’s ranking procedure (Tukey, 1977) adapted to the circular setting (Buttarazzi et al, 2018).

Usage

CircularTukeyDepth(x)
CircularTukeyDepth(x)

Arguments

x

numeric; a vector of class circular in units=c("degrees", "radians")

Value

depth

a two column matrix of circular observations with corresponding depth value

median

the depth-based circular median as an object of class circular

iqr

the depth-based circular inter-quartile range as an object of class circular

Author(s)

Davide Buttarazzi

References

Buttarazzi D., Pandolfo G., Porzio G.C. (2018). A boxplot for circular data, Biometrics.

Tukey, J. W. (1977). Exploratory Data Analysis. MA: AddisonWesley, Reading (UK).

Examples

#install.packages("circular")
require(circular)
data1 <- rvonmises(50, circular(pi/2), 5)
CircularTukeyDepth(data1)
#install.packages("circular")
require(circular)
data1 <- rvonmises(50, circular(pi/2), 5)
CircularTukeyDepth(data1)

Circular Violin Plot

Description

The CircularViolinPlot function produces a violin plot for circular data, with support for full, outer, inner, and two-halves representations. It provides options for displaying confidence intervals, notches, outliers, and additional graphical elements.

Usage

CircularViolinPlot(
    data,
    data2 = NULL,
    type = c("full", "outer", "inner", "two_halves"),
    notch = FALSE,
    beans = c("none", "all", "inliers", "outliers", "outlier_points"),
    outlier_point_color = "red",
    outlier_point_size = 2,
    outlier_point_alpha = 0.8,
    show_ci_interval = TRUE,
    show_notch_cutout = TRUE,
    show_notch_guides = FALSE,
    r0 = 1,
    density_scale = 0.3,
    vonMises_grid = NULL,
    bw = NULL,
    bw2 = NULL,
    kernel = "vonmises",
    fill = "skyblue",
    fill2 = "darkorange",
    alpha = 0.75,
    alpha2 = 0.75,
    fill_outlier = NULL,
    fill2_outlier = NULL,
    alpha_outlier = 0.2,
    alpha2_outlier = 0.2,
    arc_color = "black",
    arc_color2 = "black",
    ci_color = "white",
    ci_color2 = "white",
    arc_thickness = 0.06,
    ci_thickness = 0.012,
    box_width_factor = 1,
    density_threshold = 0,
    cutoff = NULL,
    cutoff2 = NULL,
    n_boot = 1000,
    ci_level = 0.95,
    notch_factor = 0.9,
    notch_guide_linetype = "solid",
    notch_guide_linewidth = 0.4,
    bean_length = 0.035,
    bean_min_size = 0.15,
    bean_max_size = 0.6,
    circle_color = "grey70",
    circle_linewidth = 0.7,
    center_point = TRUE,
    center_point_color = "black",
    center_point_size = 1.8,
    title = "",
    xlim = c(-1.5, 1.5),
    ylim = c(-1.5, 1.5)
)
CircularViolinPlot(
    data,
    data2 = NULL,
    type = c("full", "outer", "inner", "two_halves"),
    notch = FALSE,
    beans = c("none", "all", "inliers", "outliers", "outlier_points"),
    outlier_point_color = "red",
    outlier_point_size = 2,
    outlier_point_alpha = 0.8,
    show_ci_interval = TRUE,
    show_notch_cutout = TRUE,
    show_notch_guides = FALSE,
    r0 = 1,
    density_scale = 0.3,
    vonMises_grid = NULL,
    bw = NULL,
    bw2 = NULL,
    kernel = "vonmises",
    fill = "skyblue",
    fill2 = "darkorange",
    alpha = 0.75,
    alpha2 = 0.75,
    fill_outlier = NULL,
    fill2_outlier = NULL,
    alpha_outlier = 0.2,
    alpha2_outlier = 0.2,
    arc_color = "black",
    arc_color2 = "black",
    ci_color = "white",
    ci_color2 = "white",
    arc_thickness = 0.06,
    ci_thickness = 0.012,
    box_width_factor = 1,
    density_threshold = 0,
    cutoff = NULL,
    cutoff2 = NULL,
    n_boot = 1000,
    ci_level = 0.95,
    notch_factor = 0.9,
    notch_guide_linetype = "solid",
    notch_guide_linewidth = 0.4,
    bean_length = 0.035,
    bean_min_size = 0.15,
    bean_max_size = 0.6,
    circle_color = "grey70",
    circle_linewidth = 0.7,
    center_point = TRUE,
    center_point_color = "black",
    center_point_size = 1.8,
    title = "",
    xlim = c(-1.5, 1.5),
    ylim = c(-1.5, 1.5)
)

Arguments

data

Numeric vector of class circular, containing the primary circular observations. The data should have units specified as degrees or radians.

data2

Optional numeric vector of class circular, containing a second set of circular observations. Required when type = "two_halves".

type

Character string specifying the plot representation. Options are "full" (default), "outer", "inner", and "two_halves".

notch

Logical; whether to display notches in the plot. Default is FALSE.

beans

Character string specifying which observations or groups should be represented by beans. Options are "none", "all", "inliers", "outliers", and "outlier_points".

outlier_point_color

Character string specifying the color of individual outlier points. Default is "red".

outlier_point_size

Numeric; size of individual outlier points. Default is 2.

outlier_point_alpha

Numeric; transparency of individual outlier points, between 0 and 1. Default is 0.8.

show_ci_interval

Logical; whether to display the confidence interval. Default is TRUE.

show_notch_cutout

Logical; whether to display the notch cutout. Default is TRUE.

show_notch_guides

Logical; whether to display guide lines associated with the notches. Default is FALSE.

r0

Numeric; radius of the reference circle. Default is 1.

density_scale

Numeric; scaling factor applied to the normalized density to determine the width of the violin. Default is 0.3.

vonMises_grid

An optional data frame containing a precomputed calibration grid generated by generate_vonmises_grid. If supplied, this grid is used for estimating the von Mises concentration parameter without regenerating the calibration grid. If NULL (default), the grid is generated automatically when required.

bw

Numeric; smoothing bandwidth used to estimate the density of data. By default, when kernel is "vonmises", the bandwidth is determined automatically.

bw2

Numeric; smoothing bandwidth used to estimate the density of data2. Default is NULL, allowing automatic selection.

kernel

Character string specifying the smoothing kernel used for density estimation. Supported options are "vonmises" and "wrappednormal", corresponding to kernels of type "K" in density.circular from the circular package.

fill

Character string specifying the fill color of the primary violin. Default is "skyblue".

fill2

Character string specifying the fill color of the second violin or half. Default is "darkorange".

alpha

Numeric; transparency of the primary violin fill, between 0 and 1. Default is 0.75.

alpha2

Numeric; transparency of the second violin fill, between 0 and 1. Default is 0.75.

fill_outlier

Character string specifying the fill color used for outliers in the primary data. Default is NULL.

fill2_outlier

Character string specifying the fill color used for outliers in the second data set. Default is NULL.

alpha_outlier

Numeric; transparency of the primary outlier fill, between 0 and 1. Default is 0.2.

alpha2_outlier

Numeric; transparency of the second outlier fill, between 0 and 1. Default is 0.2.

arc_color

Character string specifying the color of the arcs of the primary violin. Default is "black".

arc_color2

Character string specifying the color of the arcs of the second violin or half. Default is "black".

ci_color

Character string specifying the color used to display the confidence interval for the primary data. Default is "white".

ci_color2

Character string specifying the color used to display the confidence interval for the second data set. Default is "white".

arc_thickness

Numeric; thickness of the violin arcs. Default is 0.06.

ci_thickness

Numeric; thickness of the confidence interval elements. Default is 0.012.

box_width_factor

Numeric; scaling factor controlling the width of the box or summary-statistic component. Default is 1.

density_threshold

Numeric; density threshold below which density values are set to zero, resulting in a narrower violin. Default is zero, meaning no additional shrinking.

cutoff

Numeric; cutoff threshold for the outlier detection rule applied to the primary data, used to clip the density. Default is NULL.

cutoff2

Numeric; cutoff threshold for the outlier detection rule applied to the second data set. Default is NULL.

n_boot

Integer; number of bootstrap iterations used to estimate confidence intervals. Default is 1000.

ci_level

Numeric; confidence level used for confidence interval estimation. Default is 0.95.

notch_factor

Numeric; scaling factor controlling the size of the notches. Default is 0.9.

notch_guide_linetype

Character string specifying the line type of the notch guide lines. Default is "solid".

notch_guide_linewidth

Numeric; line width of the notch guide lines. Default is 0.4.

bean_length

Numeric; parameter controlling the length of the bean elements. Default is 0.035.

bean_min_size

Numeric; minimum size of the bean elements. Default is 0.15.

bean_max_size

Numeric; maximum size of the bean elements. Default is 0.6.

circle_color

Character string specifying the color of the reference circle. Default is "grey70".

circle_linewidth

Numeric; line width of the reference circle. Default is 0.7.

center_point

Logical; whether to display the center point. Default is TRUE.

center_point_color

Character string specifying the color of the center point. Default is "black".

center_point_size

Numeric; size of the center point. Default is 1.8.

title

Character string specifying the plot title. Default is an empty string.

xlim

Numeric vector of length two specifying the horizontal axis limits. Default is c(-1.5, 1.5).

ylim

Numeric vector of length two specifying the vertical axis limits. Default is c(-1.5, 1.5).

Value

outliers: A vector of class circular in radians, containing observations classified as outliers as lying in the outlying region.
cutoff: The cutoff threshold used by the outlier detection rule to clip the density. The violin plot is truncated at the furthest non-outliers.
statistics: A data frame containing circular summary statistics including the circular median, first and third quartiles.

Author(s)

Davide Buttarazzi, Houyem Demni Demni et al. (2026), Robust measures of dispersion for circular data with an anomaly detection rule. Under review. Demni et al. (2026), Notched violin plots for circular data. In: Martella, F., Arima, S., Marino, M.F., Mollica, C. (eds) Statistical Science: From Theory to Applied Research I. SIS-FENStatS 2026. Italian Statistical Society Series on Advances in Statistics. Springer, Cham. https://doi.org/10.1007/978-3-032-30873-3 10.

Examples

require(circular)
x <- rvonmises(50, circular(pi/2), 5)
v = generate_vonmises_grid(rho_seq = seq(0.01, 0.99, by = 0.05))
CircularViolinPlot(x, vonMises_grid = v)

# Specify a plot representation explicitly
CircularViolinPlot(x, vonMises_grid = v, type = "full")

# Example with two data sets
y <- rvonmises(50, circular(pi), 5)
CircularViolinPlot(x, data2 = y, vonMises_grid = v, type = "two_halves")

require(circular)
x <- rvonmises(50, circular(pi/2), 5)
v = generate_vonmises_grid(rho_seq = seq(0.01, 0.99, by = 0.05))
CircularViolinPlot(x, vonMises_grid = v)

# Specify a plot representation explicitly
CircularViolinPlot(x, vonMises_grid = v, type = "full")

# Example with two data sets
y <- rvonmises(50, circular(pi), 5)
CircularViolinPlot(x, data2 = y, vonMises_grid = v, type = "two_halves")

Elbow angles for a healthy patient

Description

Angular gait measurements for a healthy patient, recorded as left-elbow angles.

Usage

data("GaitData")
data("GaitData")

Format

A matrix of class circular, with angles in radians. The supplied object includes a column label left_elbow_angle_healthy.

Details

This dataset was supplied in the file ‘GaitData.RData’. The observations use the circular class from the circular package.

Source

Pace et al. 2026, Markerless gait analysis and circular statistics: a case study in Parkinson's disease classification. In: Sintorn, I.M., Pal, U., Lu, S. (eds), Pattern Recognition. ICPR 2026 International Workshops. Lecture Notes in Computer Science, vol. 17110. Springer, Cham. DOI: 10.1007/978-3-032-39379-1 4.

Kour, N., Arora, S.: Vision-based gait dataset for gait analysis. In: 2022 2nd Inter-national Conference on Advance Computing andInnovativeTechnologiesinEngi-neering,pp.2163-2168.IEEE(2022)

Examples

data("GaitData")
str(e_healthy)
summary(e_healthy)
data("GaitData")
str(e_healthy)
summary(e_healthy)

Elbow angles for a Parkinson patient

Description

Angular gait measurements for a Parkinson parkinson, recorded as left-elbow angles.

Usage

data("GaitData")
data("GaitData")

Format

A matrix of class circular, with angles in radians. The supplied object includes a column label left_elbow_angle_parkinson.

Details

This dataset was supplied in the file ‘GaitData.RData’. The observations use the circular class from the circular package.

Source

Kour, N., Arora, S.: Vision-based gait dataset for gait analysis. In: 2022 2nd Inter-national Conference on Advance Computing andInnovativeTechnologiesinEngi-neering,pp.2163-2168.IEEE(2022)

Examples

data("GaitData")
str(e_parkinson)
summary(e_parkinson)
data("GaitData")
str(e_parkinson)
summary(e_parkinson)

Robust estimation of the concentration parameter kappa of the von Mises distribution from robust measures of dispersion

Description

Robust estimation of the concentration parameter of the von Mises distribution from robust measures of dispersion (Demni et al, 2026)

Usage

EstimateKappa(X, stat = c("CLMS","CMAD", "CLTS"), results_grid = NULL)
EstimateKappa(X, stat = c("CLMS","CMAD", "CLTS"), results_grid = NULL)

Arguments

X

numeric; a vector of class circular

stat

character; one of the available estimators c("CLMS","CMAD", "CLTS"), respectively Circular Median Absolute Deviation, Circular Least Median Spread, Circular Least Trimmed Standard deviation.

results_grid

a dataframe of a custom grid of kappa used for interpolation. If NULL (default), the grid is handled automatically.

Value

CSD

the estimated circular standard deviation based on the robust measures of dispersion

kappa

the estimated kappa based on the estimated robust circular standard deviation

Author(s)

Davide Buttarazzi, Houyem Demni

References

Demni et al. (2026), Robust measures of dispersion for circular data with an anomaly detection rule. Under review.

Examples

#install.packages("circular")
require(circular)
data1 <- rvonmises(50, circular(pi/2), 5)
EstimateKappa(data1)
#install.packages("circular")
require(circular)
data1 <- rvonmises(50, circular(pi/2), 5)
EstimateKappa(data1)

Robust estimation of the concentration parameter of the von Mises-Fisher distribution

Description

Robust estimation of the concentration parameter of the von Mises-Fisher distribution (Ko, 1992).

Usage

EstimateKappaKo(X)
EstimateKappaKo(X)

Arguments

X

numeric; a vector of class circular in units=c("radians")

Value

A numeric value

Author(s)

Davide Buttarazzi

References

Ko, D. (1992), Robust estimation of the concentration parameter of the von Mises-Fisher distribution. Ann. Stat. 20(2) 917-928

Examples

#install.packages("circular")
require(circular)
data1 <- rvonmises(50, circular(pi/2), 5)
EstimateKappaKo(data1)
#install.packages("circular")
require(circular)
data1 <- rvonmises(50, circular(pi/2), 5)
EstimateKappaKo(data1)

Robust estimation of the scale parameter sigma of the Wrapped-Normal distribution from the robust measures of dispersion

Description

Robust estimation of the scale parameter sigma of the Wrapped-Normal distribution from the robust measures of dispersion (Demni et al, 2026)

Usage

EstimateSigma(X, stat = c("CLMS", "CMAD", "CLTS"), results_grid = NULL)
EstimateSigma(X, stat = c("CLMS", "CMAD", "CLTS"), results_grid = NULL)

Arguments

X

numeric; a vector of class circular

stat

character; one of the available estimators c("CLMS", "CMAD", "CLTS"), respectively Circular Median Absolute deviation, Circular Least Median Spread, Circular Least Trimmed Standard deviation.

results_grid

a dataframe of a custom grid of kappa used for interpolation. If NULL (default), the grid is handled automatically.

Value

CSD

the estimated circular standard deviation based on the robust measures of dispersion

sigma

the estimated sigma based on the estimated robust circular standard deviation

Author(s)

Davide Buttarazzi, Houyem Demni

References

Demni et al. (2026), Robust measures of dispersion for circular data with an anomaly detection rule. Under review.

Examples

#install.packages("circular")
require(circular)
data1 <- rvonmises(25, circular(pi/2), 5)
g=generate_results_grid_sigma(sigma_seq = seq(0.1, 1.5, by = 0.1))
EstimateSigma(data1, results_grid = g)
#install.packages("circular")
require(circular)
data1 <- rvonmises(25, circular(pi/2), 5)
g=generate_results_grid_sigma(sigma_seq = seq(0.1, 1.5, by = 0.1))
EstimateSigma(data1, results_grid = g)

Generate a Calibration Grid for Estimating the Wrapped Normal Scale Parameter

Description

Generates a calibration grid relating robust measures of circular dispersion to the circular standard deviation (CSD) and the scale parameter ( $\sigma$ ) of a wrapped normal 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 wrapped normal scale parameter.

Usage

generate_results_grid_sigma(
  sigma_seq = seq(0.1, 1.5, by = 0.0005)
)
generate_results_grid_sigma(
  sigma_seq = seq(0.1, 1.5, by = 0.0005)
)

Arguments

sigma_seq

A numeric vector of positive values of the wrapped normal scale parameter $\sigma$ for which the calibration grid is generated. The default sequence ranges from 0.1 to 1.5 in increments of 0.0005.

Details

The calibration grid is constructed by evaluating the dispersion statistics over a sequence of wrapped normal distributions with different values of $\sigma$ .

For a given observed dataset, the estimation procedure first computes one of the following robust measures of circular dispersion: CircularMAD, CircularLMS, or CircularLTS, depending on the selected statistic.

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:

sigma: Values of the wrapped normal scale parameter.
rho: The mean resultant length of the wrapped normal distribution, calculated as $\exp(-\sigma^2/2)$ .
CSD: The circular standard deviation, calculated as $\sqrt{2(1-\rho)}$ .
CMAD: The calibration values obtained using the 0.75 quantile of the centred wrapped normal distribution, for the CMAD-based estimation procedure.
CLMS: The calibration values obtained using the 0.75 quantile of the centred wrapped normal distribution, for the CLMS-based estimation procedure.
CLTS: The calibration values obtained using the CLTS-based estimation procedure.

Examples

# Generate a smaller calibration grid
grid <- generate_results_grid_sigma(
  sigma_seq = seq(0.1, 1.5, length.out = 50)
)

head(grid)
# Generate a smaller calibration grid
grid <- generate_results_grid_sigma(
  sigma_seq = seq(0.1, 1.5, length.out = 50)
)

head(grid)

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.

Usage

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

Examples


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

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

head(custom_grid)

Spring wind directions

Description

Wind-direction measurements for spring, stored as circular observations.

Usage

data("Wind_directions")
data("Wind_directions")

Format

A matrix of class circular, with angles in radians. The supplied object includes a column label Spring2010.

Details

This dataset was supplied in the file ‘Wind_directions.RData’. The observations use the circular class from the circular package.

Source

Demni et al. (2026), Notched violin plots for circular data. In: Martella, F., Arima, S., Marino, M.F., Mollica, C. (eds) Statistical Science: From Theory to Applied Research I. SIS-FENStatS 2026. Italian Statistical Society Series on Advances in Statistics. Springer, Cham. https://doi.org/10.1007/978-3-032-30873-3 10.

Examples

data("Wind_directions")
str(Spring)
summary(Spring)
data("Wind_directions")
str(Spring)
summary(Spring)

Summer wind directions

Description

Wind-direction measurements for summer, stored as circular observations.

Usage

data("Wind_directions")
data("Wind_directions")

Format

A matrix of class circular, with angles in radians. The supplied object includes a column label Summer2010.

Details

This dataset was supplied in the file ‘Wind_directions.RData’. The observations use the circular class from the circular package.

Source

Examples

data("Wind_directions")
str(Summer)
summary(Summer)
data("Wind_directions")
str(Summer)
summary(Summer)

Package 'bpDir'

Help Index

AxialBoxplot

Description

Usage

Arguments

Details

Value

Author(s)

References

Examples

Circular Box-and-Wisker Plot

Description

Usage

Arguments

Details

Value

Author(s)

References

Examples

Compute the robust measure of circular spread: the Circular Least Median Spread (CLMS)

Description

Usage

Arguments

Value

Author(s)

References

See Also

Examples

Compute the robust measure of circular spread: the Circular Least Trimmed Standard deviation (CLTS)

Description

Usage

Arguments

Value

Author(s)

References

See Also

Examples

Compute the robust measure of circular spread: the Circular Median Absolute Deviation (CMAD)

Description

Usage

Arguments

Value

Author(s)

References

See Also

Examples

Circular Tukey Depth

Description

Usage

Arguments

Value

Author(s)

References

See Also

Examples

Circular Violin Plot

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

Elbow angles for a healthy patient

Description

Usage

Format

Details

Source

See Also

Examples

Elbow angles for a Parkinson patient

Description

Usage

Format

Details

Source

See Also

Examples