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Statistical estimators of the distribution of a set of vectors

Usage

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

mean(x, ...)

sd(x, ...)

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

var(x, ...)

# 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