confidence {tectonicr} | R Documentation |
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: |
w |
(optional) Weights. A vector of positive numbers and of the same
length as |
axial |
logical. Whether the data are axial, i.e. pi-periodical
( |
na.rm |
logical value indicating whether |
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)