spml.mle: MLE of some circular distributions

In Directional: A Collection of Functions for Directional Data Analysis

MLE of some circular distributions

Description

MLE of some circular distributions.

Usage

spml.mle(x, rads = FALSE, tol = 1e-07)
wrapcauchy.mle(x, rads = FALSE, tol = 1e-07)
circexp.mle(x, rads = FALSE, tol = 1e-06)
circbeta.mle(x, rads = FALSE)
cardio.mle(x, rads = FALSE)
ggvm.mle(phi, rads = FALSE)
cipc.mle(x, rads = FALSE, tol = 1e-6)
gcpc.mle(x, rads = FALSE)
mmvm.mle(x, N, rads = FALSE)

Arguments

x	A numerical vector with the circular data. They can either be expressed in radians or in degrees.
phi	A numerical vector with the circular data. They can either be expressed in radians or in degrees.
N	The number of modes to consider in the multi-modal von Mises distribution.
rads	If the data are in radians set this to TRUE.
tol	The tolerance level to stop the iterative process of finding the MLEs.

Details

The parameters of the bivariate angular Gaussian (spml.mle), wrapped Cauchy, circular exponential, cardioid, circular beta, geometrically generalised von Mises, CIPC (reparametrised version of the wrapped Cauchy), GCPC (generalisation of the CIPC) and multi-modal von Mises distributions are estimated. For the Wrapped Cauchy, the iterative procedure described by Kent and Tyler (1988) is used. The Newton-Raphson algortihm for the angular Gaussian is described in the regression setting in Presnell et al. (1998). The circular exponential is also known as wrapped exponential distribution.

Value

A list including:

iters	The iterations required until convergence.
loglik	The value of the maximised log-likelihood.
param	A vector consisting of the estimates of the two parameters, the mean direction for both distributions and the concentration parameter \kappa and the \rho for the von Mises (and the multi-modal von Mises) and wrapped Cauchy respectively. For the circular beta this contains the mean angle and the \alpha and \beta parameters. For the cardioid distribution this contains the \mu and \rho parameters. For the generalised von Mises this is a vector consisting of the \zeta, \kappa, \mu and \alpha parameters of the generalised von Mises distribution as described in Equation (2.7) of Dietrich and Richter (2017).
gamma	The norm of the mean vector of the angular Gaussian, the CIPC and the GCPC distributions.
mu	The mean vector of the angular Gaussian, the CIPC and the GCPC distributions.
mumu	In the case of "angular Gaussian distribution this is the mean angle in radians.
circmu	In the case of the CIPC and the GCPC this is the mean angle in radians.
rho	For the GCPC distribution this is the eigenvalue of the covariance matrix, or the covariance determinant.
lambda	The lambda parameter of the circular exponential distribution.

Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris [e-mail].

References

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 I_s(x). Computational Statistics, 27(1): 177–190.

Presnell Brett, Morrison Scott P. and Littell Ramon C. (1998). Projected multivariate linear models for directional data. Journal of the American Statistical Association, 93(443): 1068–1077.

Kent J. and Tyler D. (1988). Maximum likelihood estimation for the wrapped Cauchy distribution. Journal of Applied Statistics, 15(2): 247–254.

Dietrich T. and Richter W. D. (2017). Classes of geometrically generalized von Mises distributions. Sankhya B, 79(1): 21–59.

https://en.wikipedia.org/wiki/Wrapped_exponential_distribution

Jammalamadaka S. R. and Kozubowski T. J. (2003). A new family of circular models: The wrapped Laplace distributions. Advances and Applications in Statistics, 3(1), 77–103.

Tsagris M. and Alzeley O. (2024). Circular and spherical projected Cauchy distributions: A Novel Framework for Circular and Directional Data Modeling. https://arxiv.org/pdf/2302.02468.pdf

Barnett M. J. and Kingston R. L. (2024). A note on the Hendrickson-Lattman phase probability distribution and its equivalence to the generalized von Mises distribution. Journal of Applied Crystallography, 57(2).

See Also

circ.summary, purka.mle, rvonmises, vmf.mle, rvmf

Examples

x <- rvonmises(1000, 3, 9)
spml.mle(x, rads = TRUE)
wrapcauchy.mle(x, rads = TRUE)
circexp.mle(x, rads = TRUE)
ggvm.mle(x, rads = TRUE)

Directional documentation built on Oct. 30, 2024, 9:15 a.m.