Directional (version 4.0)

MLE of the angular central Gaussian distribution: MLE of the angular central Gaussian distribution

Description

MLE of the angular central Gaussian distribution.

Usage

acg(x, tol = 1e-07)

Arguments

x

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

tol

The tolerance value at which to terminate the iterations.

Value

A list including:

iter

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

cova

The estimated covatriance matrix.

Details

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.

References

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

See Also

rbingham, rfb, f.rbing, fb.saddle

Examples

# NOT RUN {
m <- c(0, 0, 0, 0)
s <- cov(iris[, 1:4])
x <- MASS::mvrnorm(500, m, s)
x <- x / sqrt( Rfast::rowsums(x^2) )
mod <- acg(x)
mod
cov2cor(mod$cova)  ## estimated covariance matrix turned into a correlation matrix
cov2cor(s)  ## true covariance matrix turned into a correlation matrix
# }