Rbar2kappa: \bar{R} to kappa conversion

In geostats: An Introduction to Statistics for Geoscientists

\bar{R} to κ conversion

Description

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

Usage

Rbar2kappa(R, p = 1)

Arguments

R	a scalar or vector of values between 0 and 1
p	the number of parameters

Details

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

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

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

Value

value(s) between 0 and +∞

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))

geostats documentation built on Jan. 7, 2023, 5:32 p.m.