MLE of the Wood bimodal distribution on the sphere {Directional}

MLE of the Wood bimodal distribution on the sphere

Description

It estimates the parameters of the Wood bimodal distribution.

Usage

wood.mle(y)

Arguments

y

A matrix containing two columns. The first one is the latitude and the second is the longitude, both expressed in degrees.

Details

The Wood distribution is fitted to some data and its parameters are estimated. It is a bimodal distribution which contains 5 parameters, just like the Kent distribution.

Value

A list including:

info

A 5 x 3 matrix containing the 5 parameters, \gamma, \delta, \alpha, \beta and \kappa along with their corresponding 95% confidence intervals all expressed in degrees.

modes

The two axis of the modes of the distribution expressed in degrees.

unitvectors

A 3 x 3 matrix with the 3 unit vectors associated with the \gamma and \delta parameters.

loglik

The value of the log-likelihood.

Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris [e-mail] and Giorgos Athineou <[e-mail]>.

References

Wood A.T.A. (1982). A bimodal distribution on the sphere. Journal of the Royal Statistical Society, Series C, 31(1): 52–58.

See Also

kent.mle, esag.mle, vmf.mle, sphereplot

Examples

x <- rvmf(100, rnorm(3), 15)
x <- euclid.inv(x)
wood.mle(x)