Directional (version 4.1)

MLE of some circular distributions with multiple samples: 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.

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.

Details

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

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

# NOT RUN {
y <- rcauchy(100, 3, 1)
x <- y 
# }
# NOT RUN {
<!-- %% (2 * pi) -->
# }
# NOT RUN {
ina <- rep(1:2, 50)
multivm.mle(x, ina)
multispml.mle(x, ina)
# }