R: von Mises Density Function

vonMises {circular} | R Documentation

## von Mises Density Function

### Description

Density, distribution function, random generation and quantiles for the von Mises circular distribution.

### Usage

    rvonmises(n, mu, kappa, control.circular=list())
    dvonmises(x, mu, kappa, log)
    pvonmises(q, mu, kappa, from=NULL, tol = 1e-020)
    qvonmises(p, mu = circular(0), kappa=NULL, from=NULL, tol = .Machine$double.eps^(0.6),
      control.circular = list(), ...)

### Arguments

`x, q, p` | a vector. The `x` and `q` objects are coerced to class `circular`.
`n` | number of observations.
`mu` | mean direction of the distribution. The object is coerced to class `circular`.
`kappa` | non-negative numeric value for the concentration parameter of the distribution.
`log` | logical; if TRUE, probabilities p are given as log(p).
`from` | if `NULL` is set to mu-pi. This is the value from which the pvonmises and qvonmises are evaluated. It should be a `circular` object.
`tol` | the precision in evaluating the distributon function or the quantile.
`control.circular` | the attribute of the resulting object.
`...` | parameters passed to `integrate`.

### Value

`dvonmises` gives the density, `pvonmises` gives the distribution function, `rvonmises` generates random deviates and `qvonmises` provides quantiles.

Since version 0.3-5 the random deviates are generated using a C code.

### Author(s)

Claudio Agostinelli, Ulric Lund and Harry Southworth

### References

Jammalamadaka, S. Rao and SenGupta, A. (2001). Topics in Circular Statistics, Section 2.2.4, World Scientific Press, Singapore.

### Examples

    data1 <- rvonmises(100, circular(0), 10, control.circular=list(units="degrees"))
    plot(data1)

    ff <- function(x) dvonmises(x, mu=circular(pi), kappa=10)
    curve.circular(ff, join=TRUE, xlim=c(-2.3, 1),
      main="Density of a VonMises Distribution \n mu=pi, kappa=10")

    ff <- function(x) pvonmises(x, mu=circular(pi), kappa=10)
    curve.circular(ff, join=FALSE, xlim=c(-2, 2), ylim=c(-2, 1),
      to=(2*pi-3*.Machine$double.eps), modulo="asis", nosort=TRUE,
      main="Probability of a VonMises Distribution \n mu=pi, kappa=10")

    plot(function(x) qvonmises(x, mu=circular(0), kappa=5), from=0, to=1)
    ##curve do not work!
    plot(function(x) qvonmises(x, mu=circular(pi), kappa=5), from=0, to=1)
    plot(function(x) qvonmises(x, mu=circular(pi), kappa=5, from=circular(pi/2)), from=0, to=1)

[Package circular version 0.4-93 Index]