Statistical estimators of the distribution of a set of vectors

Usage

# S3 method for class 'spherical'
mean(x, w = NULL, na.rm = TRUE)

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

# S3 method for class 'spherical'
sd(x, w = NULL, na.rm = TRUE)

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

# S3 method for class 'spherical'
var(x, w = NULL, na.rm = TRUE)

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", or "Plane".
w: numeric. Optional weights for each observation.
na.rm: logical. Whether NA values should be removed before the computation proceeds.
...: arguments passed to function call
alpha: numeric. Significance level for the confidence angle (default is 0.05 for a 95% confidence angle).

Details

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

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

delta returns the cone angle containing ~63% of the data (in degree 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.

confidence_angle returns the semi-vertical angle \(q\) about the mean \(\mu\) (in degree 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).

Examples

set.seed(20250411)
x <- rvmf(100, mu = Line(120, 50), k = 5)
mean(x)
#> Line object (n = 1):
#>   azimuth    plunge 
#> 115.21007  52.67744 
var(x)
#> [1] 0.224176
delta(x)
#> [1] 39.1202
rdegree(x)
#> [1] 0.551648
sd_error(x)
#> [1] 4.01451
confidence_angle(x)
#> [1] 6.965534
estimate_k(x)
#> [1] 4.673486

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