# jonespewsey: Jones and Pewsey Density Function In circular: Circular Statistics

## Description

Density for the Jones and Pewsey circular distribution.

## Usage

 1 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.

The density

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

 1 2 3 4 5 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")) ) 

### Example output

Attaching package: ‘circular’

The following objects are masked from ‘package:stats’:

sd, var


circular documentation built on May 1, 2019, 7:57 p.m.