sd.circular {circular}

Circular Standard Deviation

Description

Returns the circular standard deviation of a vector of circular data which is defined as the square root of minus 2 times the log of the mean resultant length divided by the number of observations.

Usage

## S3 method for class 'circular'
sd(x, na.rm = FALSE, ...)

Arguments

x

a vector. The object is coerced to class circular.

na.rm

logical, indicating if NA's should be omitted.

...

further arguments passed to or from other methods.

Details

Computes the circular standard deviation as defined by Mardia (1972)

\sqrt{-2\ln r}

where r is the mean resultant length of the data.

Value

Returns the circular standard deviation.

Author(s)

Claudio Agostinelli and Jean-Olivier Irisson

References

Mardia, K.V. (1972) Statistics of Directional Data. Academic Press, London, sec. 26.5, p. 617

Fisher, N.I. (1993) Statistical analysis of circular data. Cambridge University Press.

Jammalamadaka, S. Rao and SenGupta, A. (2001). Topics in Circular Statistics, Section 1.3, World Scientific Press, Singapore.

Zar, J H (2010). Biostatistical analysis. Prentice Hall. sec. 26.5, p. 617

See Also

var.circular, angular.deviation, mean.circular, rho.circular and summary.circular.

Examples

# Compute the circular standard deviation of a random
# sample of observations from a von Mises distribution
x <- rvonmises(n=100, mu=circular(0, units="degrees"), kappa=10)
sd(x)