mle.vonmises: von Mises Maximum Likelihood Estimates

In circular: Circular Statistics

von Mises Maximum Likelihood Estimates

Description

Computes the maximum likelihood estimates for the parameters of a von Mises distribution: the mean direction and the concentration parameter.

Usage

mle.vonmises(x, mu=NULL, kappa=NULL, bias=FALSE, control.circular=list())
## S3 method for class 'mle.vonmises'
print(x,
    digits = max(3, getOption("digits") - 3), ...)

Arguments

x	a vector. The object is coerced to class circular.
mu	if NULL the maximum likelihood estimate of the mean direction is calculated. If provided it is coerced to a class circular.
kappa	if NULL the maximum likelihood estimate of the concentration parameter is calculated.
bias	logical, if TRUE, the estimate for kappa is computed with a bias corrected method. Default is FALSE, i.e. no bias correction.
control.circular	the attribute of the resulting objects (mu)
digits	integer indicating the precision to be used.
...	further arguments passed to or from other methods.

Details

Best and Fisher (1981) show that the MLE of kappa is seriously biased when both sample size and mean resultant length are small. They suggest a bias-corrected estimate for kappa when n < 16.

Value

Returns a list with the following components:

call	the match.call result.
mu	the estimate of the mean direction or the value supplied as an object of class circular.
kappa	the estimate of the concentration parameter or the value supplied
se.mu	the standard error for the estimate of the mean direction (0 if the value is supplied) in the same units of mu.
se.kappa	the standard error for the estimate of the concentration parameter (0 if the value is supplied).
est.mu	TRUE if the estimator is reported.
est.kappa	TRUE if the estimator is reported.

Author(s)

Claudio Agostinelli and Ulric Lund

References

Jammalamadaka, S. Rao and SenGupta, A. (2001). Topics in Circular Statistics, Section 4.2.1, World Scientific Press, Singapore.

Best, D. and Fisher N. (1981). The bias of the maximum likelihood estimators of the von Mises-Fisher concentration parameters. Communications in Statistics - Simulation and Computation, B10(5), 493-502.

See Also

mean.circular and mle.vonmises.bootstrap.ci

Examples

x <- rvonmises(n=50, mu=circular(0), kappa=5)
mle.vonmises(x) # estimation of mu and kappa
mle.vonmises(x, mu=circular(0)) # estimation of kappa only

circular documentation built on Sept. 8, 2023, 6:03 p.m.