# dJp: Jones and Pewsey (2005)'s circular distribution In sdetorus: Statistical Tools for Toroidal Diffusions

## Description

Computes the circular density of Jones and Pewsey (2005).

## Usage

 ```1 2 3``` ```dJp(x, mu, kappa, psi, const = NULL) constJp(mu, kappa, psi, M = 200) ```

## Arguments

 `x` evaluation angles, not necessary in [π,π). `mu` circular mean. `kappa` non-negative concentration parameter. `psi` shape parameter, see details. `const` normalizing constant, computed with `constJp` if not provided. `M` grid size for computing the normalizing constant by numerical integration.

## Details

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.

## Value

A vector of the same length as `x` containing the density.

## References

Jammalamadaka, S. R. and SenGupta, A. (2001) Topics in Circular Statistics. World Scientific, Singapore. doi: 10.1142/4031

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. doi: 10.1198/016214505000000286

## Examples

 ```1 2 3 4 5 6``` ```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]) } ```

sdetorus documentation built on Aug. 19, 2021, 9:06 a.m.