Reparameterised von Mises-Fisher distribution

Density, distribution function, and random generation for the von Mises-Fisher distribution.

Usage

dvmf2(x, theta, log = FALSE)

rvmf2(n, theta)

Arguments

x: unit vector or matrix (with each row being a unit vector) of evaluation points
theta: direction and concentration vector. The direction of theta determines the mean direction on the sphere. The norm of theta is the concentration parameter of the distribution.
log: logical; if TRUE, densities are returned on the log scale.
n: number of random values to return.

Value

dvmf gives the density and rvm generates random deviates.

Details

In this parameterisation, \(\theta = \kappa \mu\), where \(\mu\) is a unit vector and \(\kappa\) is the concentration parameter.

dvmf2 allows for automatic differentiation with RTMB. rvmf2 is imported from movMF::rmovMF.

Examples

set.seed(123)
# single parameter set
theta <- c(1,2,3)
x <- rvmf2(1, theta)
d <- dvmf2(x, theta)

# vectorised over parameters
theta <- matrix(theta, nrow = 1)
theta <- theta[rep(1,10), ]
x <- rvmf2(10, theta)
d <- dvmf2(x, theta)