Rbar2kappa {geostats}R Documentation

Rˉ\bar{R} to κ\kappa conversion

Description

Converts the empirical concentration parameter Rˉ\bar{R} to the von-Mises concentration parameter κ\kappa.

Usage

Rbar2kappa(R, p = 1)

Arguments

R

a scalar or vector of values between 0 and 1

p

the number of parameters

Details

Rˉ\bar{R} and κ\kappa are two types of concentration parameter that are commonly used in directional data analysis. κ\kappa is one of the parameters of the parametric von Mises distribution, which is difficult to estimate from the data. Rˉ\bar{R} is easier to calculate from data. Rbar2kappa converts Rˉ\bar{R} to κˉ\bar{\kappa} using the following approximate empirical formula:

κ=Rˉ(p+1Rˉ2)1Rˉ2\kappa = \frac{\bar{R}(p+1-\bar{R}^2)}{1-\bar{R}^2}

where pp marks the number of parameters in the data space (1 for circle, 2 for a sphere).

Value

value(s) between 0 and ++\infty

References

Banerjee, A., et al. “Clustering on the unit hypersphere using von Mises-Fisher distributions.” Journal of Machine Learning Research 6.Sep (2005): 1345-1382.

Examples

data(striations,package='geostats')
Rbar2kappa(Rbar(striations,degrees=TRUE))

[Package geostats version 1.6 Index]