rvm {BAMBI} | R Documentation |

## The univariate von Mises distribution

### Description

The univariate von Mises distribution

### Usage

```
rvm(n, kappa = 1, mu = 0)
dvm(x, kappa = 1, mu = 0, 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. |

`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 von Mises distribution has density

`f(x) = 1/(2\pi I_0 (\kappa)) \exp(\kappa \cos(x - mu))`

where `I_0 (\kappa)`

denotes the modified Bessel function of the first kind with order 0 evaluated at the point `\kappa`

.

### Value

`dvm`

gives the density and `rvm`

generates random deviates.

### Examples

```
kappa <- 1:3
mu <- 0:2
x <- 1:10
n <- 10
# when x and both parameters are scalars, dvm returns a single density
dvm(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
dvm(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 dvm returns a vector of with ith element being the
# density evaluated at x with parameter values kappa[i] and mu[i]
dvm(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 dvm 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]
dvm(x, kappa, mu)
# when parameters are all scalars, number of observations generated by rvm is n
rvm(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 rvm is the same as the length of
# the recycled vectors
rvm(n, kappa, mu)
```

*BAMBI*version 2.3.5 Index]