| Type: | Package |
| Title: | Sampling from the von Mises-Fisher Distribution |
| Version: | 0.0.3 |
| Date: | 2024-03-20 |
| Description: | Provides fast sampling from von Mises-Fisher distribution using the method proposed by Andrew T.A Wood (1994) <doi:10.1080/03610919408813161>. |
| License: | GPL-3 |
| Encoding: | UTF-8 |
| BugReports: | https://github.com/ahoundetoungan/vMF/issues |
| URL: | https://github.com/ahoundetoungan/vMF |
| Depends: | R (≥ 3.5.0) |
| Imports: | Rcpp |
| LinkingTo: | Rcpp, RcppArmadillo |
| Suggests: | movMF, rbenchmark, knitr, rmarkdown, ggplot2, ddpcr |
| RoxygenNote: | 7.2.3 |
| VignetteBuilder: | knitr |
| NeedsCompilation: | yes |
| Packaged: | 2024-03-09 11:33:59 UTC; haache |
| Author: | Aristide Houndetoungan [cre, aut] |
| Maintainer: | Aristide Houndetoungan <ahoundetoungan@gmail.com> |
| Repository: | CRAN |
| Date/Publication: | 2024-03-09 23:30:02 UTC |
Normalization constant of von Mises - Fisher distribution.
Description
CpvMF returns the normalization constant of von Mises - Fisher density.
Usage
CpvMF(p, k)
Arguments
p |
as sphere dimension. |
k |
as the intensity parameter. |
Details
The probability density function of the von Mises - Fisher distribution is defined by :
f(z|theta) = C_p(|theta|)\exp{(z theta)}
|theta| is the intensity parameter and \frac{theta}{|theta|} the mean directional parameter. The normalization constant C_p() depends
on the Bessel function of the first kind. See more details here.
Value
the normalization constant.
References
Wood, A. T. (1994). Simulation of the von Mises Fisher distribution. Communications in statistics-simulation and computation, 23(1), 157-164. doi:10.1080/03610919408813161.
Hornik, K., & Grun, B. (2014). movMF: An R package for fitting mixtures of von Mises-Fisher distributions. Journal of Statistical Software, 58(10), 1-31. doi:10.18637/jss.v058.i10.
See Also
Examples
CpvMF(2,3.1)
PDF of the von Mises - Fisher distribution.
Description
dvMF computes the density of the von Mises - Fisher distribution, given a set of spherical coordinates and the distribution parameters.
Usage
dvMF(z, theta)
Arguments
z |
as the set of points at which the spherical coordinate will be evaluated. z may be an one row matrix or vector if it contain one spherical coordinates or a matrix whose each row is one spherical coordinates. |
theta |
as the distribution parameter. |
Details
The probability density function of the von Mises - Fisher distribution is defined by :
f(z|theta) = C_p(|theta|)\exp{(z theta)}
|theta| is the intensity parameter and \frac{theta}{|theta|} the mean directional parameter. The normalization constant C_p() depends
on the Bessel function of the first kind. See more details here.
Value
the densities computed at each point
Author(s)
Aristide Houndetoungan <ariel92and@gmail.com>
References
Wood, A. T. (1994). Simulation of the von Mises Fisher distribution. Communications in statistics-simulation and computation, 23(1), 157-164. doi:10.1080/03610919408813161.
Hornik, K., & Grun, B. (2014). movMF: An R package for fitting mixtures of von Mises-Fisher distributions. Journal of Statistical Software, 58(10), 1-31. doi:10.18637/jss.v058.i10.
See Also
rvMF and CpvMF
Examples
{}
# Draw 1000 vectors from vM-F with parameter 1, (1,0)
z <- rvMF(1000,c(1,0))
# Compute the density at these points
dvMF(z,c(1,0))
# Density of (0,1,0,0) with the parameter 3, (0,1,0,0)
dvMF(c(0,1,0,0),c(0,3,0,0))
Sample from von Mises - Fisher distribution.
Description
rvMF returns random draws from von Mises - Fisher distribution.
Usage
rvMF(size, theta)
Arguments
size |
as the number of draws needed. |
theta |
as the distribution parameter. |
Details
The parameter theta is such that dim(theta) is the sphere dimension, |theta| the intensity parameter and \frac{theta}{|theta|} the mean directional parameter.
Value
A matrix whose each row is a random draw from the distribution.
References
Wood, A. T. (1994). Simulation of the von Mises Fisher distribution. Communications in statistics-simulation and computation, 23(1), 157-164. doi:10.1080/03610919408813161.
Hornik, K., & Grun, B. (2014). movMF: An R package for fitting mixtures of von Mises-Fisher distributions. Journal of Statistical Software, 58(10), 1-31. doi:10.18637/jss.v058.i10.
Examples
# Draw 1000 vectors from vM-F with parameter 1, (1,0)
rvMF(1000,c(1,0))
# Draw 10 vectors from vM-F with parameter sqrt(14), (2,1,3)
rvMF(10,c(2,1,3))
# Draw from the vMF distribution with mean direction proportional
# to c(1, -1) and concentration parameter 3
rvMF(10, 3 * c(1, -1) / sqrt(2))