GenVonMises {circular}

Generalized Von Mises Density Function

Description

Density for the Generalized von Mises circular distribution.

Usage

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

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.

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.

Value

The density

Author(s)

Federico Rotolo

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"))
  )