Directional (version 7.0)

Density of a mixture of rotationally symmetric distributions: Density of a mixture of rotationally symmetric distributions

Description

Density of a mixture of rotationally symmetric distributions.

Usage

dmixvmf(y, probs, mu, k, logden = FALSE)
dmixspcauchy(y, probs, mu, rho, logden = FALSE)
dmixpkbd(y, probs, mu, rho, logden = FALSE)

Value

A vector with the (log) density values of y.

Arguments

y

A matrix with unit vectors.

probs

This is avector with the mixing probability of each group.

mu

A matrix with the mean direction of each group.

k

A vector with the concentration parameter of each group.

rho

A vector with the concentration parameter of each group.

logden

If you the logarithm of the density values set this to TRUE.

Author

Michail Tsagris.

R implementation and documentation: Michail Tsagris .

Details

The function computes the density for a given mixture of von Mises-Fisher, spherical Cauchy or Poisson kernel-based distributions.

References

Kurt Hornik and Bettina Grun (2014). movMF: An R Package for Fitting Mixtures of von Mises-Fisher Distributions http://cran.r-project.org/web/packages/movMF/vignettes/movMF.pdf

Tsagris M., Papastamoulis P. and Kato S. (2024). Directional data analysis using the spherical Cauchy and the Poisson kernel-based distribution. https://arxiv.org/pdf/2409.03292.

See Also

mixvmf.mle, rvmf, bic.mixvmf

Examples

k <- runif(3, 4, 6)
probs <- c(0.2, 0.5, 0.3)
mu <- matrix(rnorm(9), ncol = 3)
mu <- mu / sqrt( rowSums(mu^2) )
x <- rmixvmf(200, probs, mu, k)$x
b <- dmixvmf(x, probs, mu, k)