rotations (version 1.6.5)

fisher.kappa: Circular variance and concentration parameter

Description

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

Usage

fisher.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 matrix-Fisher distribution. For numerical stability, a maximum \(\kappa\) of 350 is returned.

mardia2000

See Also

Fisher

Examples

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