vmf {DirStats}

Von Mises–Fisher distribution utilities

Description

Maximum likelihood estimation for the von Mises–Fisher distribution and evaluation of density mixtures.

Usage

kappa_ml(data, min_kappa = 1e-04, max_kappa = 100, ...)

mu_ml(data)

d_mixvmf(x, mu, kappa, p, norm = FALSE)

Arguments

data

directional data, a matrix of size c(n, q + 1).

min_kappa, max_kappa

minimum and maximum kappas to look for the maximum likelihood estimate.

...

further parameters passed to uniroot.

x

evaluation points, a matrix of size c(nx, q + 1).

mu, kappa, p

mixture parameters. mu is the mean matrix of size c(length(p), q + 1), kappa is vector of length(p) concentration parameters, and p is the vector of mixture proportions.

norm

enforce normalization of x internally? Defaults to FALSE.

Value

Estimated vector mean (mu_ml) or concentration parameter (kappa_ml). A vector of length nx for d_mixvmf.

Examples

# Sample
n <- 50
q <- 2
samp <- rotasym::r_vMF(n = n, mu = c(1, rep(0, q)), kappa = 2)

# Estimates
mu_ml(samp)
kappa_ml(samp)

# Mixture
x <- to_cir(seq(0, 2 * pi, l = 200))
dens <- d_mixvmf(x = x, mu = rbind(c(-1, 0), c(0, 1), c(1, 0)),
                 kappa = 1:3, p = c(0.5, 0.2, 0.3))
plot(to_rad(x), dens, type = "l")