circular (version 0.3-7)

mle.vonmises: 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.

Value

• Returns a list with the following components:
• call
  the match.call().
• 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.

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.

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