MLE of some circular distributions with multiple samples {Rfast2}

MLE of some circular distributions with multiple samples

Description

MLE of some circular distributions with multiple samples.

Usage

multivm.mle(x, ina, tol = 1e-07, ell = FALSE)
multispml.mle(x, ina, tol = 1e-07, ell = FALSE)

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.

ina

A numerical vector with discrete numbers starting from 1, i.e. 1, 2, 3, 4,... or a factor variable. Each number denotes a sample or group. If you supply a continuous valued vector the function will obviously provide wrong results.

tol

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

ell

Do you want the log-likelihood returned? The default value is FALSE.

Details

The parameters of the von Mises and of the bivariate angular Gaussian distributions are estimated for multiple samples.

Value

A list including:

iters

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

loglik

A vector with the value of the maximised log-likelihood for each sample.

mi

For the von Mises, this is a vector with the means of each sample. For the angular Gaussian (spml), a matrix with the mean vector of each sample

ki

A vector with the concentration parameter of the von Mises distribution at each sample.

gi

A vector with the norm of the mean vector of the angular Gaussian distribution at each sample.

Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris [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

colspml.mle, purka.mle

Examples

y <- rcauchy(100, 3, 1)
x <- y 
ina <- rep(1:2, 50)
multivm.mle(x, ina)
multispml.mle(x, ina)