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)
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.
Value
numeric. Concentration of a von Mises distribution
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)
#> [1] 10.69211
est.kappa.MLE(x, w)
#> [1] 10.33191
