Package 'svmf'

The Scaled von Mises–Fisher Distribution

Description

Functions to perform maximum likelihood estimation of and random value simulation from the scaled von Mises–Fisher distribution. For more information see Scealy and Wood (2019).

Details

Package:	svmf
Type:	Package
Version:	1.0
Date:	2026-06-11

Maintainers

Michail Tsagris <[email protected]>.

Author(s)

Michail Tsagris [email protected]

References

Scealy J.L. and Wood A.T.A. (2019). Scaled von Mises-Fisher distributions and regression models for paleomagnetic directional data. Journal of the American Statistical Association, 114(528): 1547–1560.

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Random value simulation from the scaled von Mises–Fisher distribution

Description

Random value simulation from the scaled von Mises–Fisher distribution.

Usage

rsvmf(n, mu, a, kappa, Gamma = NULL)

Arguments

n	The sample size.
mu	The mean direction.
a	The vector of alphas.
kappa	The concentration parameter.
Gamma	The matrix with the $\gamma$ vectors.

Value

A matrix with the simulated data.

Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris [email protected].

References

Scealy J.L. and Wood A.T.A. (2019). Scaled von Mises-Fisher distributions and regression models for paleomagnetic directional data. Journal of the American Statistical Association, 114(528): 1547–1560.

See Also

svmf.mle

Examples

mu <- rnorm(3)
mu <- mu / sqrt( sum(mu^2) )
a <- c(1, 3, 1/3)
y <- rsvmf(1000, mu, a, 20)
svmf.mle(y)

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Maximum likelihood estimation of the scaled von Mises–Fisher distribution

Description

Maximum likelihood estimation of the scaled von Mises–Fisher distribution.

Usage

svmf.mle(y, a1 = 1, maxit_outer = 100, maxit_V = 500, tol = 1e-6)

Arguments

y	A numerical matrix with the (hyper-)spherical observations.
a1	The value of the $\alpha_1$ parameter is set to 1 , as suggested by Scealy and Wood (2019).
maxit_outer	The maximum number of iterations to perform.
maxit_V	The maximum number of iterations to perform to estimate the $V$ matrix.
tol	The tolerance value until convergence of the log-likelihood.

Value

A list including:

mu	The estimated mean direction.
kappa	The estimated concentration parameter.
a	The estimated vector of alphas, the first value is 1, by default.
loglik	the log-likelihood value.
Gamma	The estimated matrix with the $\gamma$ vectors. The first column of this matrix is the mean direction.

Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris [email protected].

References

Scealy J.L. and Wood A.T.A. (2019). Scaled von Mises-Fisher distributions and regression models for paleomagnetic directional data. Journal of the American Statistical Association, 114(528): 1547–1560.

See Also

rsvmf

Examples

mu <- rnorm(3)
mu <- mu / sqrt( sum(mu^2) )
a <- c(1, 3, 1/3)
y <- rsvmf(1000, mu, a, 20)
svmf.mle(y)

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