rotations (version 1.6.5)

cayley.kappa: Circular variance and concentration parameter

Description

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

Usage

cayley.kappa(nu)

Value

Concentration parameter corresponding to nu.

Arguments

nu

circular variance

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 mardia2000 for more details. This function translates the circular variance \(\nu\) into the corresponding concentration parameter \(\kappa\) for the Cayley distribution.

mardia2000

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)