rotations (version 1.5)

cayley.kappa: Circular variance and concentration parameter

Description

Return the concentration parameter that corresponds to a given circular variance.

Usage

cayley.kappa(nu)

Arguments

nu

circular variance

Value

Concentration parameter corresponding to nu.

Details

The concentration parameter $\kappa$ does not translate across circular distributions. A commonly used measure of spread in circular distributions that does translate is the circular variance defined as $\nu=1-E[cos(r)]$ where $E[cos(r)]$ is the mean resultant length. See Mardia et al. (2000) for more details. This function translates the circular variance $\nu$ into the corresponding concentration parameter $\kappa$ for the Cayley distribution.

References

Mardia K and Jupp P (2000). Directional statistics. John Wiley & Sons, Chichester, England.

See Also

Cayley

Examples

#Find the concentration parameter for circular variances 0.25, 0.5, 0.75
 cayley.kappa(0.25)
 cayley.kappa(0.5)
 cayley.kappa(0.75)