MLE of the angular central Gaussian distribution

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Description

MLE of the angular central Gaussian distribution

Usage

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acg(x)

Arguments

x

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

Details

There is a constraint on the estimated covariance matrix, that its trace is equal to the number of variables. An iterative algorithm takes place and convergence is guaranteed.

Value

A list including:

iter

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

cova

The estimated covatriance matrix.

Author(s)

Michail Tsagris R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Giorgos Athineou <athineou@csd.uoc.gr>

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

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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

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