R: Generalized Von Mises Density Function

GenVonMises {circular} | R Documentation

## 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)=exp[κ_1 \cos(x-μ_1) + κ_2 \cos{2(x-μ_2) }] / [2 π G_0(δ,κ_1,κ_2)],

for 0 <= x < 2 π, where δ=(μ_1-μ_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"))
      )

[Package circular version 0.4-93 Index]