# wrappednormal: Wrapped Normal Density Function In circular: Circular Statistics

## Description

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

## Usage

 ```1 2 3 4 5 6 7 8 9``` ```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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22``` ```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) ```

circular documentation built on May 1, 2019, 7:57 p.m.