R: Wrapped Normal Density Function

wrappedNormal {circular} | R Documentation

## Wrapped Normal Density Function

### Description

Density, and random generation for the wrapped normal circular distribution.

### Usage

    rwrappednormal(n, mu = circular(0), rho = NULL, sd = 1,
      control.circular = list())
    dwrappednormal(x, mu = circular(0), rho = NULL, sd = 1,
      K = NULL, min.k = 10)
    pwrappednormal(q, mu = circular(0), rho = NULL, sd = 1,
      from = NULL, K = NULL, min.k = 10, ...)
    qwrappednormal(p, mu = circular(0), rho = NULL, sd = 1,
      from = NULL, K = NULL, min.k = 10, tol = .Machine$double.eps^(0.6),
      control.circular = list(), ...)

### Arguments

`x, q` | vector of quantiles. The object is coerced to class `circular`.
`p` | vector of probabilities.
`n` | number of observations.
`mu` | mean direction of the distribution as a `circular` object.
`rho` | concentration parameter of the distribution. `rho` must be in the interval from 0 to 1.
`sd` | standard deviation of the (unwrapped) normal distribution.
`from` | if `NULL` is set to mu-pi. This is the value from which the pwrappednormal and qwrappednormal are evaluated. It should be a `circular` object.
`K` | number of terms to be used in approximating the density.
`min.k` | minimum number of terms used in approximating the density.
`tol` | passed to `uniroot`.
`control.circular` | the attribute of the resulting object.
`...` | parameters passed to `integrate`.

### Value

`dwrappednormal` gives the density and `rwrappednormal` generates random deviates, `pwrappednormal` gives the distribution function, and `qwrappednormal` provides quantiles.

### Author(s)

Claudio Agostinelli and Ulric Lund

### References

Jammalamadaka, S. Rao and SenGupta, A. (2001). Topics in Circular Statistics, Section 2.2.7, World Scientific Press, Singapore.

### Examples

    data1 <- rwrappednormal(100, mu=circular(0), rho=0.7,
      control.circular=list(units="degrees"))
    plot(data1)

    ff <- function(x) dwrappednormal(x, mu=circular(pi), rho=0.7)
    curve.circular(ff, join=TRUE, xlim=c(-1.5, 1),
      main="Density of a Wrapped Normal Distribution \n mu=pi, rho=0.7")

    ff <- function(x) pwrappednormal(x, mu=circular(pi), rho=0.7)
    curve.circular(ff, join=FALSE, xlim=c(-2, 2), ylim=c(-2, 2),
      to=(2*pi-3*.Machine$double.eps), modulo="asis", nosort=TRUE,
      main="Probability of a Wrapped Normal Distribution \n mu=pi,
      rho=0.7, from=0")

    ff <- function(x) pwrappednormal(x, mu=circular(pi), rho=0.7, from=circular(pi))
    curve.circular(ff, join=FALSE, xlim=c(-2, 2), ylim=c(-2, 2), from=-pi,
      to=(pi-3*.Machine$double.eps), modulo="asis", nosort=TRUE,
      main="Probability of a Wrapped Normal Distribution \n mu=pi,
      rho=0.7, from=pi")

    plot(qwrappednormal, from=0, to=1)
    plot(function(x) qwrappednormal(p=x, mu=circular(pi)), from=0, to=1)

[Package circular version 0.4-93 Index]