Directional (version 5.3)

MLE of some circular distributions: 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)

Arguments

x

A numerical vector with the circular data. They must be expressed in radians.

phi

A numerical vector with the circular data.

rads

If the data are in radians set this to TRUE.

tol

The tolerance level to stop the iterative process of finding the MLEs.

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 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 distribution.

mu

The mean vector of the angular Gaussian distribution.

mumu

In the case of "angular Gaussian distribution this is the mean angle in radians.

lambda

The lambda parameter of the circular exponential distribution.

Details

The parameters of the bivariate angular Gaussian (spml.mle), wrapped Cauchy, circular exponential, cardioid, circular beta and geometrically generalised 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.

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 Is(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

See Also

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

Examples

# NOT RUN {
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)
# }