# genvonmises: Generalized Von Mises Density Function In circular: Circular Statistics

## Description

Density for the Generalized von Mises circular distribution.

## Usage

 1 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.

The density

Federico Rotolo

## References

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

## Examples

 1 2 3 4 5 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")) ) 

### 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.