acg.mle: MLE of (hyper-)spherical distributions

MLE of (hyper-)spherical distributionsR Documentation

MLE of (hyper-)spherical distributions


MLE of (hyper-)spherical distributions.


vmf.mle(x, tol = 1e-07)
multivmf.mle(x, ina, tol = 1e-07, ell = FALSE)
acg.mle(x, tol = 1e-07)
iag.mle(x, tol = 1e-07)



A matrix with directional data, i.e. unit vectors.


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.


This is for the multivmf.mle only. Do you want the log-likelihood returned? The default value is TRUE.


The tolerance value at which to terminate the iterations.


For the von Mises-Fisher, the normalised mean is the mean direction. For the concentration parameter, a Newton-Raphson is implemented. For the angular central Gaussian distribution there is a constraint on the estimated covariance matrix; its trace is equal to the number of variables. An iterative algorithm takes place and convergence is guaranteed. Newton-Raphson for the projected normal distribution, on the sphere, is implemented as well. Finally, the von Mises-Fisher distribution for groups of data is also implemented.


For the von Mises-Fisher a list including:


The maximum log-likelihood value.


The mean direction.


The concentration parameter.

For the multi von Mises-Fisher a list including:


A vector with the maximum log-likelihood values if ell is set to TRUE. Otherwise NULL is returned.


A matrix with the group mean directions.


A vector with the group concentration parameters.

For the angular central Gaussian a list including:


The number if iterations required by the algorithm to converge to the solution.


The estimated covariance matrix.

For the spherical projected normal a list including:


The number of iteration required by the Newton-Raphson.


A matrix with two rows. The first row is the mean direction and the second is the mean vector. The first comes from the second by normalising to have unit length.


A vector with the elements, the norm of mean vector, the log-likelihood and the log-likelihood of the spherical uniform distribution. The third value helps in case you want to do a log-likleihood ratio test for uniformity.


Michail Tsagris R implementation and documentation: Michail Tsagris <>


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.

Tyler D. E. (1987). Statistical analysis for the angular central Gaussian distribution on the sphere. Biometrika 74(3): 579-589.

Paine P.J., Preston S.P., Tsagris M and Wood A.T.A. (2017). An Elliptically Symmetric Angular Gaussian Distribution. Statistics and Computing (To appear).

See Also

racg, vm.mle, rvmf


m <- c(0, 0, 0, 0)
s <- cov(iris[, 1:4])
x <- racg(100, s)
mod <- acg.mle(x)
res<-cov2cor(mod$cova)  ## estimated covariance matrix turned into a correlation matrix
res<-cov2cor(s)  ## true covariance matrix turned into a correlation matrix
x <- rbind( rvmf(100,rnorm(4), 10), rvmf(100,rnorm(4), 20) )
a <- multivmf.mle(x, rep(1:2, each = 100) )

Rfast documentation built on Nov. 9, 2023, 5:06 p.m.