rwnorm {BAMBI} | R Documentation |

## The univariate Wrapped Normal distribution

### Description

The univariate Wrapped Normal distribution

### Usage

```
rwnorm(n = 1, kappa = 1, mu = 0)
dwnorm(x, kappa = 1, mu = 0, int.displ, log = FALSE)
```

### Arguments

`n` |
number of observations. Ignored if at least one of the other parameters have length k > 1, in which case, all the parameters are recycled to length k to produce k random variates. |

`kappa` |
vector of concentration (inverse-variance) parameters; |

`mu` |
vector of means. |

`x` |
vector of angles (in radians) where the densities are to be evaluated. |

`int.displ` |
integer displacement. If |

`log` |
logical. Should the log density be returned instead? |

### Details

If `mu`

and `kappa`

are not specified they assume the default values of `0`

and `1`

respectively.

The univariate wrapped normal distribution has density

`f(x) = \sqrt(\kappa/(2\pi)) \sum \exp(-\kappa/2 (x - \mu(2\pi\omega))^2)`

where the sum extends over all integers `\omega`

,
and is approximated by a sum over `\omega`

in `\{-M, -M+1, ..., M-1, M \}`

if `int.displ = `

`M`

.

### Value

`dwnorm`

gives the density and `rwnorm`

generates random deviates.

### Examples

```
kappa <- 1:3
mu <- 0:2
x <- 1:10
n <- 10
# when x and both parameters are scalars, dwnorm returns a single density
dwnorm(x[1], kappa[1], mu[1])
# when x is a vector but both the parameters are scalars, dmv returns a vector of
# densities calculated at each entry of x with the same parameters
dwnorm(x, kappa[1], mu[1])
# if x is scalar and at least one of the two paraemters is a vector, both parameters are
# recycled to the same length, and dwnorm returns a vector of with ith element being the
# density evaluated at x with parameter values kappa[i] and mu[i]
dwnorm(x[1], kappa, mu)
# if x and at least one of the two paraemters is a vector, x and the two parameters are
# recycled to the same length, and dwnorm returns a vector of with ith element being the
# density at ith element of the (recycled) x with parameter values kappa[i] and mu[i]
dwnorm(x, kappa, mu)
# when parameters are all scalars, number of observations generated by rwnorm is n
rwnorm(n, kappa[1], mu[1])
# when at least one of the two parameters is a vector, both are recycled to the same length,
# n is ignored, and the number of observations generated by rwnorm is the same as the length
# of the recycled vectors
rwnorm(n, kappa, mu)
```

*BAMBI*version 2.3.5 Index]