Computes the circular density of Jones and Pewsey (2005).
dJp(x, mu, kappa, psi, const = NULL)constJp(mu, kappa, psi, M = 200)
A vector of the same length as x
containing the density.
evaluation angles, not necessary in
circular mean.
non-negative concentration parameter.
shape parameter, see details.
normalizing constant, computed with constJp
if not
provided.
grid size for computing the normalizing constant by numerical integration.
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.
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. tools:::Rd_expr_doi("10.1198/016214505000000286")
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])
}
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