confidence: Confidence Interval around the Mean Direction of Circular...

In tectonicr: Analyzing the Orientation of Maximum Horizontal Stress

Confidence Interval around the Mean Direction of Circular Data after Batschelet (1971)

Description

Probabilistic limit on the location of the true or population mean direction, assuming that the estimation errors are normally distributed.

Usage

confidence_angle(x, conf.level = 0.95, w = NULL, axial = TRUE, na.rm = TRUE)

confidence_interval(x, conf.level = 0.95, w = NULL, axial = TRUE, na.rm = TRUE)

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.

Details

The confidence angle gives the interval, i.e. plus and minus the confidence angle, around the mean direction of a particular sample, that contains the true mean direction under a given level of confidence.

Value

Angle in degrees

References

• Batschelet, E. (1971). Recent statistical methods for orientation data. "Animal Orientation, Symposium 1970 on Wallops Island". Amer. Inst. Biol. Sciences, Washington.

• Mardia, K.V. (1972). Statistics of Directional Data: Probability and Mathematical Statistics. London: Academic Press. (p. 146)

• Davis (1986) Statistics and data analysis in geology. 2nd ed., John Wiley & Sons.

• Jammalamadaka, S. Rao and Sengupta, A. (2001). Topics in Circular Statistics, Sections 3.3.3 and 3.4.1, World Scientific Press, Singapore.

See Also

mean_resultant_length(), circular_sd_error()

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_angle(finland_stria, axial = FALSE)
confidence_interval(finland_stria, axial = FALSE)

data(san_andreas)
data("nuvel1")
PoR <- subset(nuvel1, nuvel1$plate.rot == "na")
sa.por <- PoR_shmax(san_andreas, PoR, "right")
confidence_angle(sa.por$azi.PoR, w = 1 / san_andreas$unc)
confidence_interval(sa.por$azi.PoR, w = 1 / san_andreas$unc)

tectonicr documentation built on June 8, 2025, 11:33 a.m.