Package 'rvMF'

von Mises–Fisher Distributed Pseudo-Random Vector Generator

Description

rvMF() generates von Mises–Fisher distributed pseudo-random vectors, without resorting to the rejection-based sampling method proposed by Wood (1994). See Kang and Oh (2024) for details. This function partly uses the code from the function Rfast::rvmf() and the article Marsaglia et al. (2004).

Usage

rvMF(n, mu, k)

Arguments

n	number of pseudo-random vectors to generate.
mu	mean direction.
k	concentration parameter. k ≥ 0.

Value

matrix where each row independently follows the specified von Mises-Fisher distribution. The number of columns equals the length of mu, and the number of rows equals n for rvMF.

References

S. Kang and H.-S. Oh. Novel sampling method for the von Mises–Fisher distribution. Statistics and Computing, 34(3):106, 2024.

K. V. Mardia and P. E. Jupp. Directional Statistics, volume 494. John Wiley & Sons, Chichester, 1999.

G. Marsaglia, W. W. Tsang, and J. Wang. Fast generation of discrete random variables. Journal of Statistical Software, 11(3):1–11, 2004.

M. Papadakis, M. Tsagris, M. Dimitriadis, S. Fafalios, I. Tsamardinos, M. Fasiolo, G. Borboudakis, J. Burkardt, C. Zou, K. Lakiotaki, and C. Chatzipantsiou. Rfast: A Collection of Efficient and Extremely Fast R Functions, 2022. https://CRAN.R-project.org/package=Rfast. R package version 2.0.6.

A. T. Wood. Simulation of the von Mises Fisher distribution. Communications in Statistics– Simulation and Computation, 23(1):157–164, 1994.

See Also

rvMFangle(), dvMFangle(), Rfast::rvmf().

Examples

rvMF(10, c(0,0,1), 10)
rvMF(10, c(1,1)/sqrt(2), 0)

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Inner Product of von Mises–Fisher Random Vector and Mean Direction

Description

These functions provide information about the distribution of an inner product between von Mises–Fisher random vector and its mean direction. Specifically, if $X$ follows a von Mises–Fisher distribution with mean direction $\mu$, the inner product $X'\mu$ will be a random variable following some distribution. See page 170 of Mardia and Jupp (1999). rvMFangle() generates random variates using the algorithm proposed in Kang and Oh (2024), and dvMFangle gives the density from this distribution. This function partly uses the code from the article Marsaglia et al. (2004).

Usage

rvMFangle(n, p, kappa)

dvMFangle(r, p, kappa)

Arguments

n	number of random vectors to generate.
p	dimension of the sphere. i.e., Sp-1, p ≥ 2.
kappa	concentration parameter. kappa > 0. Setting kappa = 0 may cause errors.
r	vector of quantiles. -1 ≤ r ≤ 1.

Value

• rvMFangle() returns a vector whose components independently follow the aforementioned distribution. The length of the result is determined by n for rvMFangle().

• dvMFangle() returns a vector of density function value. The length of the result is determined by the length of r for dvMFangle().

References

S. Kang and H.-S. Oh. Novel sampling method for the von Mises–Fisher distribution. Statistics and Computing, 34(3):106, 2024.

K. V. Mardia and P. E. Jupp. Directional Statistics, volume 494. John Wiley & Sons, Chichester, 1999.

G. Marsaglia, W. W. Tsang, and J. Wang. Fast generation of discrete random variables. Journal of Statistical Software, 11(3):1–11, 2004.

See Also

rvMF() wrapper of rvMFangle().

Examples

rvMFangle(10, 2, 10)
rvMFangle(10, 3, 0.1)
dvMFangle(seq(-1,1,by=0.01), 2, 10)
dvMFangle(seq(0,1,by=0.01), 3, 0.1)

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