maxwell.kappa {rotations}

Circular variance and concentration parameter

Description

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

Usage

maxwell.kappa(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 modified Maxwell-Boltzmann distribution. For numerical stability, a maximum \kappa of 1000 is returned.

Value

Concentration parameter corresponding to nu.

See Also

Maxwell

Examples

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