genvonmises: Generalized Von Mises Density Function

Description Usage Arguments Details Value Author(s) References Examples

Description

Density for the Generalized von Mises circular distribution.

Usage

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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

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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.