circular (version 0.5-1)

JonesPewsey: Jones and Pewsey Density Function

Description

Density for the Jones and Pewsey circular distribution.

Usage

djonespewsey(x, mu, kappa, psi)

Value

The density

Arguments

x

a vector. The object is coerced to class circular.

mu

direction parameter of the distribution. The object is coerced to class circular.

kappa

non-negative concentration parameter of the distribution.

psi

real shape parameter.

Author

Federico Rotolo

Details

The JonesPewsey distribution has density $$ f(x)=\frac{(\cosh(\kappa\psi) + \sinh(\kappa\psi)\cos(x-\mu))^{1/\psi}} {2\pi P_{1/\psi}(\cosh(\kappa\psi))}, $$ for \(0 \le x < 2\pi\), where \(P_{1/\psi}(\cdot)\) is the associated Legendre function of the first kind, degree \(1/\psi\) and order 0.

References

Jones , M.C. and Pewsey, A. (2005). A family of symmetric distributions on the circle. J. Am. Statist. Assoc. 100, 1422-1428

Examples

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"))
  )