Directional (version 4.0)

MLE of the spherical projected normal distribution: MLE of the spherical projected normal distribution

Description

MLE of the spherical projected normal distribution.

Usage

iag.mle(y, tol = 1e-07)

Arguments

y

A matrix with the data expressed in Euclidean coordinates, i.e. unit vectors.

tol

The tolerance to accept that the E-M algorithm used to estimate the concentration parameter has converged.

Value

A list including:

iters

The number of iteration required by the Newton-Raphson.

mesi

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.

param

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.

kappa

The concentration parameter.

Details

MLE of the projected normal distribution, on the sphere, is implemented.

References

Mardia, K. V. and Jupp, P. E. (2000). Directional statistics. Chicester: John Wiley & Sons.

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

See Also

ESAGmle, spml.mle, acg, circ.summary

Examples

# NOT RUN {
x <- as.matrix(iris[,1:3])
x <- x / sqrt( rowSums(x^2) )
iag.mle(x)
# }