MLE of some circular distributions with multiple samples.
multivm.mle(x, ina, tol = 1e-07, ell = FALSE)
multispml.mle(x, ina, tol = 1e-07, ell = FALSE)A list including:
The iterations required until convergence. This is returned in the wrapped Cauchy distribution only.
A vector with the value of the maximised log-likelihood for each sample.
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
A vector with the concentration parameter of the von Mises distribution at each sample.
A vector with the norm of the mean vector of the angular Gaussian distribution at each sample.
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.
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.
The tolerance level to stop the iterative process of finding the MLEs.
Do you want the log-likelihood returned? The default value is FALSE.
Michail Tsagris.
R implementation and documentation: Michail Tsagris mtsagris@uoc.gr.
The parameters of the von Mises and of the bivariate angular Gaussian distributions are estimated for multiple samples.
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 \(I_s(x)\). 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.
colspml.mle, purka.mle
y <- rcauchy(100, 3, 1)
x <- y
ina <- rep(1:2, 50)
multivm.mle(x, ina)
multispml.mle(x, ina)
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