R: Jones and Pewsey Density Function

JonesPewsey {circular} | R Documentation

## Jones and Pewsey Density Function

### Description

Density for the Jones and Pewsey circular distribution.

### Usage

    djonespewsey(x, mu, kappa, psi)

### 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.

### Details

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.

### Value

The density

### Author(s)

Federico Rotolo

### References

Jones , M.C. and Pewsey, A. (2005). A family of simmetric 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"))
      )

[Package circular version 0.4-93 Index]