tectonicr (version 0.4.8)

estimate-kappa: Concentration parameter of von Mises distribution

Description

Estimates the concentration parameter of a von Mises distribution, given a set of angular measurements.

Usage

est.kappa.MLE(x, w = NULL, bias = FALSE)
est.kappa(x, w = NULL, p = 2)

Value

numeric. Concentration of a von Mises distribution

Arguments

x

numeric. angles in degrees

w

numeric. weightings

bias

logical parameter determining whether a bias correction is used in the computation of the MLE. Default for bias is FALSE for no bias correction.

p

integer. Number of parameters in the data space: 2 for circle (the default), 3 for a sphere.

Details

est.kappa.MLE() is the maximum likelihood estimate for MLE for \(\kappa\).

est.kappa() uses an approximation based on the empirical equation: $$\kappa = \frac{\bar{R}(p-\bar{R}^2)}{1-\bar{R}^2} $$ where \(\bar{R}\) is the mean resultant length and \(p\) is the dimensionality of the data (2 for circular data).

Examples

set.seed(123)
x <- rvm(100, 90, 10)
w <- weighting(runif(100, 0, 10))

est.kappa(x, w)

est.kappa.MLE(x, w)