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Circular (directional) descriptive statistics

Source: R/dir_stats_circ.R
dir_stats_circ.Rd

Computes descriptive statistics for a sample of angular measurements (azimuths or orientations) using circular statistics. Optionally pulls the data column from a data frame. Handles both vectorial data (azimuths, 0°–360°) and axial data (strikes or lineations, 0°–180°) via the dir argument, and returns the mean direction, resultant length, circular variance, circular standard deviation, circular dispersion, concentration parameter, and a confidence cone for the mean direction.

Usage

dir_stats_circ(x, data = NULL, dir = 1, conf.level = 0.95)

Arguments

x

Numeric vector of angles in degrees, or an unquoted column name when data is supplied.

data

A data frame (or tibble) containing the column referenced by x. Default NULL (use x directly as a vector).

dir

Integer. Data type: 1 for vectorial data (full 360° range, default); 0 for axial data (180° range, e.g. strike or foliation— angles are doubled internally and the mean is halved back).

conf.level

Numeric. Confidence level for the mean-direction cone of confidence. Default 0.95.

Value

A one-row data frame with the following columns:

theta.hat

Mean direction in degrees (0°–360°).

N

Sample size.

R

Length of the resultant vector.

Rbar

Mean resultant length (R / N); ranges from 0 (uniform) to 1 (perfectly concentrated).

circ.var

Circular variance (1 − Rbar).

circ.sd

Circular standard deviation.

circ.disp

Circular dispersion.

kappa

Estimated concentration parameter of the von Mises distribution.

cone

Half-width of the conf.level confidence cone around the mean direction (degrees).

References

Fisher, N. I. (1993). Statistical analysis of circular data. Cambridge University Press.

Davis, J. C. (2002). Statistics and data analysis in geology (3rd ed). J. Wiley.

Swan, A. R. H., & Sandilands, M. (1995). Introduction to geological data analysis. Blackwell Science.

See also

Other directional statistics: dir_aov_spher_ax(), dir_aov_spher_vec(), dir_stats_spher(), rose_diag_circ(), rose_diag_spher()

Examples

angles = c(255, 239, 222, 231, 199, 271, 222, 274, 228, 246,
           177, 199, 257, 201, 237, 209, 216, 180, 182, 250,
           219, 196, 197, 246, 218, 235, 232, 243, 232, 180,
           231, 254, 242, 149, 212, 210, 230, 205, 220, 268)
# Vectorial data supplied as a plain vector
dir_stats_circ(angles)
#>   theta.hat  N     R   Rbar circ.var circ.sd circ.disp kappa cone
#> 1     223.2 40 35.61 0.8901   0.1099  0.4825    0.2355 4.847 8.58

# Axial data (strikes)
dir_stats_circ(angles, dir = 0)
#>   theta.hat  N     R   Rbar circ.var circ.sd circ.disp kappa cone
#> 1      44.5 40 25.07 0.6268   0.3732  0.9666     1.066 1.623 8.84

# Using tidy column selection from a data frame
df <- data.frame(azi = angles)
dir_stats_circ(azi, data = df, conf.level = 0.90)
#>   theta.hat  N     R   Rbar circ.var circ.sd circ.disp kappa cone
#> 1     223.2 40 35.61 0.8901   0.1099  0.4825    0.2355 4.847 7.19