Column-wise MLE of some circular distributions {MLE}

Column-wise MLE of some circular distributions

Description

Column-wise MLE of some circular distributions.

Usage

colcirc.mle(x, distr = "vm", tol = 1e-07, maxiters = 100, parallel = FALSE)

Arguments

x

A numerical matrix with the circular data. They must be expressed in radians.

distr

The type of distribution to fit, "vm" stands for the von Mises and "spml" is the angular Gaussian distribution.

tol

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

maxiters

The maximum number of iterations to implement. This is for the "spml" only.

parallel

Should the computations take place in parallel? This is for the "spml" only.

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 matrix with two, columns. The first one contains the parameters of the distribution and the second columns contains the log-likelihood values.

Author(s)

Michail Tsagris and Sofia Piperaki.

R implementation and documentation: Michail Tsagris [e-mail] and Sofia Piperaki [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

circ.mle,

Examples

x <- matrix( rnorm(100 * 10, 3, 1), ncol = 10)
x <- x / sqrt( rowSums(x^2) )
res <- colcirc.mle(x, distr = "spml")