MLE of some circular distributions {Rfast}

MLE of some circular distributions

Description

MLE of some circular distributions.

Usage

vm.mle(x, tol = 1e-09)
spml.mle(x, tol = 1e-09, maxiters = 100)
wrapcauchy.mle(x, tol = 1e-09)

Arguments

x

A numerical vector with the circular data. They must be expressed in radians. For the "spml.mle" this can also be a matrix with two columns, the cosinus and the sinus of the circular data.

tol

The tolerance level to stop the iterative process of finding the MLEs.

maxiters

The maximum number of iterations to implement.

Details

The parameters of the von Mises, the bivariate angular Gaussian and wrapped Cauchy distributions are estimated. For the Wrapped Cauchy, the iterative procedure described by Kent and Tyler (1988) is used. As for the von Mises distribution, we use a Newton-Raphson to estimate the concentration parameter. The angular Gaussian is described, in the regression setting in Presnell et al. (1998).

Value

A list including:

iters

The iterations required until convergence. This is returned in the wrapped Cauchy distribution only.

loglik

The value of the maximised log-likelihood.

param

A vector consisting of the estimates of the two parameters, the mean direction for both distributions and the concentration parameter kappa and the rho for the von Mises and wrapped Cauchy respectively.

gamma

The norm of the mean vector of the angualr Gaussian distribution.

mu

The mean vector of the angular Gaussian distribution.

Author(s)

Michail Tsagris and Stefanos Fafalios

R implementation and documentation: Michail Tsagris <[e-mail]> and Stefanos Fafalios <[e-mail]>

References

Mardia K. V. and Jupp P. E. (2000). Directional statistics. Chicester: John Wiley & Sons.

Sra S. (2012). A short note on parameter approximation for von Mises-Fisher distributions: and a fast implementation of Is(x). Computational Statistics, 27(1): 177-190.

Presnell Brett, Morrison Scott P. and Littell Ramon C. (1998). Projected multivariate linear models for directional data. Journal of the American Statistical Association, 93(443): 1068-1077.

Kent J. and Tyler D. (1988). Maximum likelihood estimation for the wrapped Cauchy distribution. Journal of Applied Statistics, 15(2): 247–254.

See Also

vmf.mle, rvonmises, rvmf

Examples

y <- rcauchy(100, 3, 1)
x <- y 
res<-vm.mle(x)
res<-spml.mle(x)
res<-wrapcauchy.mle(x)
x <- NULL