vMFangle {rvMF}

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., S^p-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)