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Confidence Interval around the Mean Direction of Circular Data after Fisher (1993)

Source: R/statistics.R
confidence_interval_fisher.Rd

For large samples (n >=25) i performs are parametric estimate based on sample_circular_dispersion(). For smaller size samples, it returns a bootstrap estimate.

Usage

confidence_interval_fisher(
  x,
  conf.level = 0.95,
  w = NULL,
  axial = TRUE,
  na.rm = TRUE,
  boot = FALSE,
  R = 1000L,
  quiet = FALSE
)

Arguments

x

numeric vector. Values in degrees.

conf.level

Level of confidence: \((1 - \alpha \%)/100\). (0.95 by default).

w

(optional) Weights. A vector of positive numbers and of the same length as x.

axial

logical. Whether the data are axial, i.e. pi-periodical (TRUE, the default) or directional, i.e. \(2 \pi\)-periodical (FALSE).

na.rm

logical value indicating whether NA values in x should be stripped before the computation proceeds.

boot

logical. Force bootstrap estimation

R

integer. number of bootstrap replicates

quiet

logical. Prints the used estimation (parametric or bootstrap).

Value

list

References

N.I. Fisher (1993) Statistical Analysis of Circular Data, Cambridge University Press.

Examples

# Example data from Davis (1986), pp. 316
finland_stria <- c(
  23, 27, 53, 58, 64, 83, 85, 88, 93, 99, 100, 105, 113,
  113, 114, 117, 121, 123, 125, 126, 126, 126, 127, 127, 128, 128, 129, 132,
  132, 132, 134, 135, 137, 144, 145, 145, 146, 153, 155, 155, 155, 157, 163,
  165, 171, 172, 179, 181, 186, 190, 212
)
confidence_interval_fisher(finland_stria, axial = FALSE)
#> Parametric estimate
#> $mu
#> [1] 129.1903
#> 
#> $conf.angle
#> [1] 10.20306
#> 
#> $conf.interval
#> [1] 118.9872 139.3933
#> 
confidence_interval_fisher(finland_stria, axial = FALSE, boot = TRUE)
#> Bootstrap estimate based on 1000 replicates
#> $mu
#> [1] 129.2051
#> 
#> $conf.angle
#> [1] 5.916165
#> 
#> $conf.interval
#> [1] 123.1004 135.4118
#> 

data(san_andreas)
data("nuvel1")
PoR <- subset(nuvel1, nuvel1$plate.rot == "na")
sa.por <- PoR_shmax(san_andreas, PoR, "right")
confidence_interval_fisher(sa.por$azi.PoR, w = 1 / san_andreas$unc)
#> Parametric estimate
#> $mu
#> [1] 138.9025
#> 
#> $conf.angle
#> [1] 2.085496
#> 
#> $conf.interval
#> [1] 136.817 140.988
#> 
confidence_interval_fisher(sa.por$azi.PoR, w = 1 / san_andreas$unc, boot = TRUE)
#> Bootstrap estimate based on 1000 replicates
#> $mu
#> [1] 140.8648
#> 
#> $conf.angle
#> [1] 0.483657
#> 
#> $conf.interval
#> [1] 140.3642 141.3747
#>