circular (version 0.5-1)

GenVonMises: Generalized Von Mises Density Function

Description

Density for the Generalized von Mises circular distribution.

Usage

dgenvonmises(x, mu1, mu2, kappa1, kappa2)

Value

The density

Arguments

x

a vector. The object is coerced to class circular.

mu1

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

mu2

secondary direction parameter. The object is coerced to class circular.

kappa1

non-negative numeric parameter of the distribution.

kappa2

non-negative numeric parameter of the distribution.

Author

Federico Rotolo

Details

The Generalized von Mises distribution has density $$ f(x)=\frac1{2\pi G_0(\delta,\kappa_1,\kappa_2)} \exp\{\kappa_1 \cos(x-\mu_1) + \kappa_2 \cos2(x-\mu_2)\}, $$ for \(0 \le x < 2\pi\), where \(\delta=(\mu_1-\mu_2)\) and \(G_0\) is the normalizing constant.

References

Gatto , R. & Jammalamadaka , S.R. (2007). The generalized von Mises distribution. Statistical Methodology 4, 341-353.

Examples

ff <- function(x) dgenvonmises(x, mu1=circular(5*pi/4), mu2=circular(pi/4), kappa1=.3, kappa2=1)
curve.circular(ff, join=TRUE, xlim=c(-1, 1), ylim=c(-1.2, 1.2),
  main="Density of a Generalized von Mises Distribution",
  xlab=expression(paste(mu,"1=5/4",pi,", ",mu2,"=",pi/4,", ",kappa,"1=0.3, ",kappa,"2=1"))
  )