Statistical estimators of the distribution of a set of vectors

Statistical estimators of the distribution of a set of vectors

Usage

sph_mean(x, na.rm = TRUE, ...)

sph_sd(x, ...)

sph_var(x, ...)

sph_confidence_angle(x, w = NULL, alpha = 0.05, na.rm = TRUE)

rdegree(x, w = NULL, na.rm = FALSE)

sd_error(x, w = NULL, na.rm = FALSE)

delta(x, w = NULL, na.rm = TRUE)

estimate_k(x, w = NULL, na.rm = FALSE)

Arguments

x

object of class "Vec3", "Line", "Ray", or "Plane".

na.rm

logical. Whether NA values should be removed before the computation proceeds.

...

arguments passed to function call

w

numeric. Optional weights for each observation.

alpha

numeric. Significance level for the confidence angle (default is 0.05 for a 95% confidence angle).

Details

sph_mean returns the spherical arithmetic mean of a set of vectors (object of class of x).

sph_var returns the spherical variance (numeric), based on resultant length (Mardia 1972).

sph_sd returns the spherical standard deviation (numeric) given as the half apical angle of a cone about the mean vector. In degrees if x is a "Plane" or "Line", or in radians if otherwise.

delta returns the half apical angle of the cone containing ~63% of the data (in degrees if x is a "Plane" or "Line", or in radians if otherwise). For enough large sample it approaches the angular standard deviation ("csd") of the Fisher statistics.

rdegree returns the degree of preferred orientation of vectors, range: (0, 1).

sd_error returns the spherical standard error (numeric). If the number of data is less than 25, if will print a additional message, that the output value might not be a good estimator.

sph_confidence_angle returns the half-apical angle \(q\) of a cone about the mean \(\mu\) (in degrees if x is a "Plane" or "Line", or in radians if otherwise). The \(100(1-\alpha)\%\) confidence interval is than given by \(\mu \pm q\).

estimate_k returns the estimated concentration of the von Mises-Fisher distribution \(\kappa\) (after Sra, 2011).

See also

projected_mean() for projected mean, geodesic_mean_line() and geodesic_mean_pair() for the geodesic mean of lines and pairs, respectively. or geodesic_mean() and geodesic_var() as a convenience wrapper for all spherical data types.

Examples

set.seed(20250411)
x <- rvmf(100, mu = Line(120, 50), k = 5)
sph_mean(x)
#> Line object (n = 1):
#>   azimuth    plunge 
#> 115.21007  52.67744 
sph_sd(x)
#> [1] 40.82336
sph_var(x)
#> [1] 0.224176
delta(x)
#> [1] 39.1202
rdegree(x)
#> [1] -0.9844835
sd_error(x)
#> [1] 4.01451
sph_confidence_angle(x)
#> [1] 6.965534
estimate_k(x)
#> [1] 4.673486

#' weights:
x2 <- Line(c(0, 0), c(0, 90))
sph_mean(x2)
#> Line object (n = 1):
#> azimuth  plunge 
#>       0      45 
sph_mean(x2, w = c(1, 2))
#> Line object (n = 1):
#>  azimuth   plunge 
#>  0.00000 63.43495 
sph_var(x2)
#> [1] 0.2928932
sph_var(x2, w = c(1, 2))
#> [1] 0.254644