dJp {sdetorus}

Jones and Pewsey (2005)'s circular distribution

Description

Computes the circular density of Jones and Pewsey (2005).

Usage

dJp(x, mu, kappa, psi, const = NULL)

constJp(mu, kappa, psi, M = 200)

Arguments

x

evaluation angles, not necessary in [\pi,\pi).

mu

circular mean.

kappa

non-negative concentration parameter.

psi

shape parameter, see details.

const

normalizing constant, computed with constJp if not provided.

M

grid size for computing the normalizing constant by numerical integration.

Details

Particular interesting choices for the shape parameter are:

• psi = -1: gives the Wrapped Cauchy as stationary density.

• psi = 0: is the sinusoidal drift of the vM diffusion.

• psi = 1: gives the Cardioid as stationary density.

Value

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

References

Jones, M. C. and Pewsey, A. (2005). A family of symmetric distributions on the circle. Journal of the American Statistical Association, 100(472):1422–1428. doi:10.1198/016214505000000286

Examples

x <- seq(-pi, pi, l = 200)
plot(x, x, type = "n", ylab = "Density", ylim = c(0, 0.6))
for (i in 0:20) {
  lines(x, dJp(x = x, mu = 0, kappa = 1, psi = -2 + 4 * i / 20),
        col = rainbow(21)[i + 1])
}