driftMixVm {sdetorus}

Drift for the mivM diffusion (circular case)

Description

Drift for the Langevin diffusion associated to a mixture of m independent von Mises (mivM) of dimension one.

Usage

driftMixVm(x, alpha, mu, sigma, p, expTrc = 30)

Arguments

x

vector with the evaluation points for the drift.

alpha

vector of length m giving the strengths of the drifts.

mu

vector of length m giving the means.

sigma

diffusion coefficient.

p

vector of length m giving the proportions. Must add to one.

expTrc

truncation for exponential: exp(x) with x <= -expTrc is set to zero. Defaults to 30.

Details

driftMixIndVm is more general, but less efficient for the circular case. See Section 2.2.4 in García-Portugués et al. (2019) for details.

Value

A vector of the same length as x containing the drift.

References

García-Portugués, E., Sørensen, M., Mardia, K. V. and Hamelryck, T. (2019) Langevin diffusions on the torus: estimation and applications. Statistics and Computing, 29(2):1–22. doi:10.1007/s11222-017-9790-2

Examples

x <- seq(-pi, pi, l = 200)
plot(x, x, type = "n", ylab = "drift")
for (i in 1:10) {
  lines(x, driftMixVm(x = x, alpha = c(2, 2),
                      mu = c(0, -pi + 2 * pi * i / 10),
                      sigma = 1, p = c(0.5, 0.5)), col = rainbow(10)[i])
}