Jones and Pewsey Density Function
Density for the Jones and Pewsey circular distribution.
djonespewsey(x, mu, kappa, psi)
The JonesPewsey distribution has density
f(x)=[(\cosh(κψ) + \sinh(κψ)\cos(x-μ))^{1/ψ}] / [2π P_{1/ψ}(\cosh(κψ))],
for 0 <= x < 2 π, where P_{1/ψ}(.) is the associated Legendre function of the first kind, degree 1/ψ and order 0.
The density
Federico Rotolo
Jones , M.C. and Pewsey, A. (2005). A family of simmetric distributions on the circle. J. Am. Statist. Assoc. 100, 1422-1428
ff <- function(x) djonespewsey(x, mu=circular(4), kappa=1.8, psi=-.6) curve.circular(ff, join=TRUE, xlim=c(-1, 1), ylim=c(-1.2, 1.2), main="Density of a JonesPewsey Distribution", xlab=expression(paste(mu,"=1.3",pi,", ",kappa,"=1.8, ",psi,"=-0.6")) )
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